Abstract
The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluidinterface and the physics involved at multiscale and macro, meso, micro and nanoscales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including NavierStokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuummolecular dynamics method is also reviewed.
Introduction
Human knowledge is getting enriched from the four billion years' worth of R & D in the natural world of plants and animals and other lower level living creatures and microorganisms, which have evolved through the ages to nicely adapt to the environment. Man has now drawn his attention to soil creatures like earthworms, dung beetle, sea animals like shark and plants and trees like lotus leaf and pastes like termites. In the nature, we see examples of effortless and efficient nonsticking movement in mud or moist soil, highspeed swimming aided by builtin dragreduction mechanism, water repellant contaminantfree surface cleaning mechanism and natural ventilation and air conditioning, [1–8]. By nature, feather of the penguin shows staying warm naturally, Figure 1 [4]. The leaf of the lotus is hydrophobic to the extent that water running across the surface of the leaf retains particles of dirt caused by a thick layer of wax on the surface and the sculpture of that surface, Figure 2 [9–11]. This forces the droplets of water to remain more or less spherical when in contact with the leaf, and reduces the tendency of other contaminants to stick to the leaf. It has been proved that water repellency causes an almost complete surface purification (selfcleaning effect): contaminating particles are picked up by water droplets or they adhere to the surface of the droplets and are then removed with the droplets as they roll off the leaves. This characteristic has been utilized in exteriorquality paint, 'Lotusan', which makes surfaces selfcleaning. Hooks occur in nature as a vast array of designs and in a diversity of animals and plants. The commercial application of this technology of 'Nature' can be found in Velcro [5] having the cheapest and most reliable bur hooksubstrate combination. There are now thousands of patents quoting Velcro. This is how the subject of biomimetics has developed. Biomimetics is the application and abstraction of biological methods, systems and good designs found in nature to the study and design of efficient and sustainable engineering systems and modern technology. The transfer of technology between lifeforms and manufactures is desirable because evolutionary pressure typically forces living organisms, including fauna and flora, to become highly optimized and efficient. Generally there are three areas in biology after which technological solutions can be modelled.

Replicating natural manufacturing methods as in the production of chemical compounds by plants and animals.

Mimicking mechanisms found in nature such as Velcro and Gecko tape.

Imitating organizational principles from social behaviour of organisms like ants, bees and microorganisms.
Russia has developed a systematic means for integrating the natural knowledge into humankind's technology using 'Teoriya Resheniya Izobretatelskikh Zadatch (TRIZ)', i.e. the theory of inventive problem solving, which provides an objective framework based on functionality for accessing solutions from other technologies and sciences. TRIZ also prevents waste of time trying to find a solution where none exists. The four main tools of TRIZ are a knowledge database arranged by function, analysis of the technical barriers to progress (contradictions), the way technology develops (ideality) and the maximization of resource usage. The biologybased technology 'Biomimetics' suggests new approaches resulting in patents and some into production:

Strain gauging based on receptors in insects [7],

Deployable structures based on flowers and leaves [12],

Tough ceramics based on motherofpearl [13],

Drag reduction based on dermal riblets on shark skin [14],

Tough composites based on fibre orientations in wood [15],

Underwater glues based on mussel adhesive [16],

Flight mechanisms based on insect flight [2],

Extrusion technology based on the spinneret of the spider [3],

Selfcleaning surfaces based on the surface of the lotus leaf [17].
The importance of Biomimetics will increase as the incidence of genetic manipulation increases and the genetic manufacturing is developed. In the result, the area between living and nonliving materials, where biology interacts with engineering, e.g. bioengineering and biomechatronics, is benefited.
There are innumerable examples of interactions with the environment and balanced and efficient heat, mass, momentum and species transfer through the microstructures in the fluid flow in the manifested living world of plants, animals and other living creatures. Biomimetics involve mimicking these interactions across the functional surfaces with the surrounding environments in the technological design. The physical nature is numerically modelled and simulated using computational fluid dynamics (CFD).
Geometrical analogy as well as physical similarity is to be studied to design technological functional surfaces imitating microstructural and biological functional surface morphologies. CFD at micro or mesoscales and other numerical methodologies are necessary for this [18–24].
The meso and microscale methods are also being developed in parallel with the continuum theorybased conventional CFD techniquesusing finite volume method (FVM) and finite element method (FEM). In the mesoscopic lattice Boltzmann method (LBM), fluid flow is simulated by tracking the development of distribution functions of assemblies of molecules. It is difficult to capture the interfacial dynamics, which is essential for multiphase flow, at the macroscopic level. LBM captures the interaction of fluid particles and is, therefore, helpful for multiphase flow with phase segregation and surface tension. Also, the LBM is computationally more efficient than molecular dynamics (MD) method since it does not track individual molecules; the solution algorithm is explicit, easy to implement and parallel computation can be done. Micro/nanoscale simulations in micro/nanoscale geometries and micro time scales are done in MD method and direct simulation of Monte Carlo (DSMD) method. Coupled macroscale simulation is being done using high performance computer (HPC). This article makes a review of the advances in multiscale biomimetic fluid flow modelling and simulation of difficult physics problems with complex biological interfaces.
Macroscopic biomimetic flow modelling
The locomotion, power and manoeuvring of aquatic animals like swimming fish having superior and efficient utilization of propulsion through a rhythmic unsteady motion of the body and fin resulting in unsteady flow control has been engineered for the transportation in the underwater vehicles. The fish senses and manipulates largescale vortices and repositions the vortices through tail motion. The timing of formation and shedding of vortices are important. CFD application by mimicking the swimming of fish and underwater dolphin kicking has been utilized to understand active drag and propulsive net thrust and this has resulted in better sailing performance, Olympic ski jumping, Formula 1 racing, Speedo's new Fastskin FSII swimsuit and an optimal kick profile in swim starts and turns. The undulatory propulsion in aquatic vertebrates is achieved by sending alternating waves down the body towards the tip of the tail and causing sinusoidal oscillation of the body, a jet in the wake and a forward thrust. Two modes of propulsive technique utilized by fish are anguilliform and carangiform, Figure 3 [25]. The carangiform mode is also termed as 'lunatetail swimming propulsion'.
The unsteady incompressible NavierStokes equations of turbulent flow are solved in the simulation by applying the Reynoldsaveraged NavierStokes (RANS) equations with usual boundary conditions to obtain the fluctuating velocity fields. The equations in Cartesian tensor form are:
where x and u are Cartesian coordinates and velocities, respectively, and t is time. Velocity u, density ρ, viscosity μ and other solution variables represent ensembleaveraged (or timeaveraged) values. Reynolds stress, is modelled and related to the mean velocity gradients by Boussinesq hypothesis. k is the turbulence kinetic energy, ε the kinetic energy dissipation rate and μ_{t} the turbulent viscosity. C is constant, σ the Prandtl number. G_{k} represents the generation of turbulence kinetic energy due to the mean velocity gradients. μ_{t} is the turbulent viscosity.
The turbulent flow induced by the fishtail oscillation is characterized by fluctuating velocity fields. The instantaneous governing equations are time averaged to reduce the computational time and complexity which is done in the form of turbulence models like the semiempirical kε workhorse turbulence model for practical engineering flow calculations.
To calculate the flow field using the dynamic mesh, the integral form of the conservation equation for a general scalar φ on an arbitrary control volume V with moving boundary is employed:
where is the flow velocity vector, is the grid velocity of the moving mesh, Γ is the diffusion coefficient, S_{φ} is the source term of φ and ∂V is the boundary of the control volume V.
The flow is characterized by spatially travelling waves of body bound vorticity. The mix between longitudinal and transverse flow features varies with the phase of oscillation and the unsteady velocity field varies throughout an oscillation cycle. The dynamic pressure distribution contour and the effect of the tail movement on the unsteady flow field of the fishlike body will show that there are high pressure zones at the rear of the body indicating strong vortex and turbulence. The kinematic parameters like Strouhal number, wavelength and oscillating frequency are based on the forward locomotion in a straight line with constant speed in the cruising direction. Figure 4 shows the computational geometric forms of (a) the Robo Tuna, (b) tuna with dorsal/ventral finlets and (c) giant danio [26]. Fish swimming kinematic data shows that the nondimensional frequencies are close to the value predicted by the instability analysis. Figure 5, from Rohr et al. [27], shows Strouhal number as a function of the Reynolds number for numerous observations of trained dolphins with good agreement between theory and experiment.
Other example of using CFD to study biomimetic fluid flow problems include simulation of air flow around flapping insect wings, numerical simulation of electroosmotic flow near earthworm surface and simulation of explosive discharge of the bombardier beetle.
Kroger [28] made a CFD simulation study of air flow around flapping insect wings. The interest in the flappingwing technique [29, 30] is growing recently due to the fact, that the developments in microtechnology permit people to think about building very small and highly manoeuvrable microaircraft that could be used for search and rescue missions or to detect harmful substances or pollutants in areas that are not accessible by or too dangerous for humans. There are three basic principles that contribute to unsteady flappingwing aerodynamics: delayed stall, rotational circulation and wake capture. However, the exact interactions between them are still subject to ongoing research by CFD simulation. Figure 6 shows surface mesh on fly body.
The dynamic mesh CFD model is used to examine critical flight simulations of normal aircraft, like the undercarriage lowering at low air speed, or the movement of sweep wings of fighter jets at high air speed. Next to flight applications, the dynamic mesh model can also simulate moving heart valves in the biomedical area, or small flapping membrane valves in microfluidics or the flow around any arbitrary moving part in other industry or sports applications.
The electroosmotic flow controlled by the NavierStokes equations near an earthworm surface has been simulated by Zu and Yan [31] numerically to understand the anti soil adhesion mechanism of earthworm. A lattice Poisson method (LPM), which is a derived form of LBM, has been employed to solve externally applied electric potential φ and charge distributions in the electric double layer along the earthworm surface. The external electric field is obtained by solving a Laplace equation. The simulation [32–35] showed that moving vortices, contributing to the anti soil adhesion, are formed near earthworm body surface by the nonuniform and variational electric force acting as lubricant. Figure 7 shows the electroosmotic flow field between the surfaces of soil and earthworm.
A biomimetic CFD study [36–39] of the bombardier beetle's explosive discharge apparatus and unique natural 'combustion' technique in its jetbased defence mechanism helps designing a short mass ejection system and a long range of spray ejection pertinent to reigniting a gas turbine aircraft engine which has cut out, when the cold outside air temperature is extremely low. The beetle can eject a hot discharge to around 200 to 300 times the length of its combustor. Figure 8 shows a bombardier beetle (brachina) ejecting its watersteam jet at 100°C forward from the tip of its abdomen (from left to right).
Hybrid molecularcontinuum fluid dynamics simulation
Nanoscale systems such as GaAsMESFETs and SiMOSFETs semiconductor devices, ultrafast (picoseconds or femtoseconds) pulsed lasers do not conform to the classical Fourier heat diffusion theory in which the mean free path of the energy carriers becomes comparable to or larger than the characteristic length scale of the particle device/system or the time scale of the processes becomes comparable to or smaller than the relaxation time of the energy carriers. Although numerical techniques like Boltzmann transport equation (BTE) or atomiclevel simulation (MD) and Monte Carlo simulation (MCS) can capture the physics in this regime, they require large computational resources. The CV hyperbolic equation, which is not subject to the Fourier law assumption of infinite thermal propagation speed, is also not free from anomalies.
Limitations of continuum description of a system
Finite difference and finite element methods serve well for continuum description of a system governed by a set of differential equations and boundary conditions. However, the problem arises when the system has atomic fabric of matter such as in the case of friction problems and phasechange problems of fluid freezing into a solid or dynamic transition such as intermittent stickslip motion [40].
The molecular dynamics (MD) method
When a system is modelled on the atomic level such as in case of MD, the motion of individual atoms or molecules is approximated. The particle motion is controlled by interaction potentials and equations of motion. MD is used for systems on the nanometre scale.
Coupling MDcontinuum
Coupling two very different descriptions of fluids at MDcontinuum interface is a serious issue. The overlapping region of two descriptions must be coupled over space as well as time giving consistent physical quantities like density, momentum and energy and their fluxes must be continuous. Quantities of particles may be averaged locally and temporally to obtain boundary conditions of continuum equations. Getting microscopic quantities from macroscopic nonunique ensembles is, however, difficult.
Coupling schemes
Several coupling schemes [40–44] have been developed and the two solutions relax in a finite overlap region before they are coupled. Equations of motion are the language of particles and these are coupled with the continuum language, i.e. the differential equations. The coupling mechanism transmits mass flux, momentum flux and energy flux across the domain boundary. If the remaining boundaries are sealed, i.e. the simulated system is closed; the coupling ensures conservation of mass, momentum and energy.
The two domains are coupled to each other by ensuring that the flux components normal to the domain boundary match. If particles flow towards the boundary, a corresponding amount of mass, momentum and energy must be fed into the continuum. Conversely, any transport in the vicinity of the boundary on the part of the continuum must provide a boundary condition for transport on the part of the particles.
Figure 9 shows the velocity and temperature profiles observed in a simulation using LennardJones particles and a NavierStokes continuum.
Smoothed particle hydrodynamics
Sousa [45] presented a scientific smoothed particle hydrodynamic (SPH) multiphysics simulation tool applicable from macro to nanoscale heat transfer. SPH [45] is a meshless particle based Lagrangian fluid dynamic simulation technique; the fluid flow is represented by a collection of discrete elements or pseudo particles. These particles are initially distributed with a specified density distribution and evolve in time according to the fluid heat, mass, species and momentum conservation equations. Flow properties are determined by an interpolation or smoothing of the nearby particle distribution with the help of a weighting function called the smoothing kernel. SPH is advantageous in (1) tracking problems dealing with multiphysics, (2) handling complex free surface and material interface, (3) parallel computing with relatively simple computer codes, (4) dealing with transient fluid and heat transport.
Following the original approach of Olfe [46] and Modest [47] in case of radiative heat transfer, Sousa [45] made the SPH numerical modelling for the ballisticdiffusive heat conduction equation. In this method, the heat carriers inside the medium are split into two components: ballistic and diffusive. The ballistic component is determined from the prescribed boundary condition and/or nanoscale heat sources and it experiences only outscattering; the transport of the scattered and excited heat carriers inside the medium is treated as diffusive component.
Intrinsic complex issues in hybrid method
The development and optimization of the performance of micro and nano fluidic devices requires numerical modelling of fluid flow inside micro and nanochannels. The nature of the phenomena involved in these devices invariably and predominantly has the interfacial interactions because of high surfacetovolume ratio and is characterized by an inherent multiscale nature [48–62]. The traditional continuum models do not capture the flow physics inside the micro and nano scale systems because they neglect the microscopic mechanisms at these scales. The MD is a microscopic model and this can be used where macroscopic constitutive equations and boundary conditions are inadequate. Figure 10 [48] shows the schematic representation of a molecular region in a hybrid simulation. The MD are well suited for the study of slip generation in the solidfluid interface and other surface properties like nanoroughness and wettability and the boundary conditions. However, high computational cost restricts the molecular simulations to their applications to nanoscale systems and time scales below microseconds. This disparity of spatial and temporal scales is overcome in the hybrid atomisticcontinuum multiscale frameworks where the molecular description models only a small part of the computational domain, since the physics of this part of the system cannot be represented by the continuum model. The boundary condition is transferred accurately and efficiently between the atomistic and continuum description in the hybrid methods. Since the microscopic description requires more degrees of freedom than the macroscopic one, the transfer of macroscopic information on a molecular simulation becomes all the more a challenging task.
MD model and the MaxwellBoltzmann velocity distribution
The MD atomistic model in the microscale framework is a deterministic method. In this model, the evolution of the molecular system is obtained by computing the trajectories of the particles based on the classical molecular model. The continuum conditions can be applied to molecular domain either by the method based on continuous rescaling of atomic velocities or by the periodic resampling method of atomistic velocities that employs velocity distribution functions such as MaxwellBoltzmann or ChapmanEnskog distribution for nonequilibrium situations of hybrid simulations in dilute gases employing geometrical decomposition and state coupling. The MaxwellBoltzmann velocity distribution is the natural velocity distribution of an atomic or molecular system in an equilibrium state defining the probability of onedimensional velocity components of an atom assuming a specific value based on temperature and the atomic mass. The reflective plane placed at the upper boundary of the boundary condition transfer region maintains every particle inside the molecular domain. This scheme is simpler than the velocity reversing scheme, but this can be applied only to incompressible flows because the normal pressure is a result of the reflected atoms.
Rescaling techniques
In the rescaling techniques, in addition to the velocity restrictions, the continuum pressure applies to the atomistic region. The normal pressure is applied through external forces generating a potential energy field. Energy is decreased because of the reduction of potential energy of the atoms moving towards the continuum boundary. The resulting energy oscillations in the molecular system are reduced by velocity reversing of the outermost atoms. This scheme is simple and robust because of uncontrolled transfer of energy. The continuum temperature to the molecular system is accomplished by an energy transfer scheme. The energy is added or removed from the microscopic system to parallel the macroscopic temperature without modifying the mean velocity of the particles. The energy transfer takes place independent of each dimension and is accomplished by the velocity vectors of the atoms [42, 61–68].
Issues related to boundary conditions in hybrid multiscaling modelling
Drikakis and Asproulis [69] applied macroscopic boundary conditions in hybrid multiscale modelling. MD microscopic simulation was employed. They employed the methods for various liquid and gas flows with heat transfer and identified specific parameters for accuracy and efficiency. Their work has shown that knowledge about boundary conditions development and application is needed in multiscale computational frameworks. Continuum temperature and velocity as well as macroscopic pressure constrain molecular domain. Inconsistent pressure can shrink the simulation domain and the particles may drift away generating errors and instabilities in the hybrid procedure. Also, the size of the regions for the application of velocity constrains is important to avoid unrealistic heat transfer across the computational domain and inconsistencies between the molecular and continuum state. Resampling frequency and the termination of the atomistic region have significant impact in the resampling techniques and these can influence trapping of particles in the constrained region and may cause deviations between the macroscopic and microscopic velocities. The domain termination needs correct continuum pressure application.
Challenge in biomimetic flow simulation
The task of imitating biological functional surfaces with variety of complex threedimensional micro and nanostructures is very challenging in biomimetic flow simulation. The transfer of biological morphologies of plants and animals by imitating both geometrical and physical similarity to technological applications is to be identified [70–127]. Studies on micro surface structures of different species are to be made by scanning electron microscope (SEM) and atomic force microscope (AFM) to imitate engineering functional surfaces. The mesoscopic LBM has been applied in studying electroosmotic driving flow within the micro thin liquid layer near an earthworm body surface [128]. The moving vortices give the effect of anti soil adhesion. Few multiphase LBM models are the pseudopotential model, the free energy model and the indexfunction model [129–132]. In LBM, effective interaction potential describes the fluidfluid interaction. Interface is introduced by modelling the Boltzmann collision operator imposing phase separation. Also, the fluidfluid interactions are represented by a body force term in Boltzmann equation. In this case, secondorder terms in the pressure tensor are removed and more realistic interfacial interactions are produced.
Hard spheres fluids, square well fluids and LennardJones fluids are model fluids in MD. The fluid flow and heat transfer in microscale and nanoscale systems get microscopic and nanoscopic insight from MD [133].
Conclusions
A comprehensive and stateoftheart review of CFD techniques for numerical modelling of some biomimetic flows at different scales has been done. Fluidfluid interfaces contacting with functional solid surfaces have been discussed. The multiphysics modelling at different scales by NavierStokes and energy equations, mesoscopic LBM, MD method and combined continuumMD method with appropriate coupling schemes have been dealt with in detail.
Abbreviations
 AFM:

atomic force microscope
 BTE:

Boltzmann transport equation
 CFD:

computational fluid dynamics
 DSMD:

direct simulation of Monte Carlo
 FEM:

finite element method
 FVM:

finite volume method
 HPC:

high performance computer
 LBM:

lattice Boltzmann method
 LPM:

lattice Poisson method
 MCS:

Monte Carlo simulation
 MD:

molecular dynamics
 RANS:

Reynoldsaveraged NavierStokes
 SEM:

scanning electron microscope
 SPH:

smoothed particle hydrodynamic
 TRIZ:

Teoriya Resheniya Izobretatelskikh Zadatch.
References
Ball P: Life's lessons in design. Nature 2001, 409: 413–416. 10.1038/35053198
Ellington CP: The novel aerodynamics of insect flight: applications to microair vehicles. J Exp Biol 1999, 202: 3439–3448.
Knight DP, Vollrath F: Liquid crystals and flow elongation in a spider's silk production line. Proc R Soc Lond B 1999, 266: 519–523. 10.1098/rspb.1999.0667
Dawson C, Vincent JFV, Jeronimidis G, Rice G, Forshaw P: Heat transfer through penguin feathers. J Theoret Biol 1999, 199: 291–295. 10.1006/jtbi.1999.0959
Velcro SA: Improvements in or relating to a method and a device for producing a velvet type fabric. Swiss patent no. 721338 1955.
Vincent JFV, Mann DL: Systematic technology transfer from biology to engineering. Philos Trans R Soc Lond A 2002, 360: 159–173. 10.1098/rsta.2001.0923
Skordos A, Chan PH, Vincent JFV, Jeronimidis G: A novel strain sensor based on the campaniform sensillum of insects. Philos Trans R Soc Lond A 2002, 360: 239–253. 10.1098/rsta.2001.0929
Vincent JFV, King MJ: The mechanism of drilling by wood wasp ovipositors. Biomimetics 1996, 3: 187–201.
Barthlott W, Neinhuis C: The Lotuseffect: nonadhesive biological and biomimetic technical surfaces. In Proceedings of 1st International Industrial Conference BIONIK. Hannover, Germany; 2004:211–214.
Barthlott W, Neinhuis C: The lotuseffect: Nature's model for selfcleaning surfaces. Int Text Bull 2001, 8: 10–12.
Barthlott W, Neinhuis C: Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta 1997, 202: 1–8. 10.1007/s004250050096
Guest SD, Pellegrino S: Inextensional wrapping of flat membranes. In Proceedings of International Seminar Structure Morphology. LMGC Universite Montpellier II, Montpellier; 1992:203–215.
Jackson AP, Vincent JFV, Turner RM: A physical model of nacre. Compos Sci Technol 1989, 36: 255–266. 10.1016/02663538(89)900249
Bechert DW, Bruse M, Hage W, Meyer R: Biological surfaces and their technological applicationlaboratory and flight experiments on drag reduction and separation control. In Proceedings of 28th AIAA Fluid Dynamics Conference. Snowmass Village, CO, USA; 1997.
Chaplin RC, Gordon JE, Jeronimidis G: Development of a novel fibrous composite material. US patent no. 4409274 1983.
Holl SM, Hansen D, Waite JH, Schaefer J: Solidstate NMR analysis of crosslinking in a mussel protein glue. Arch Biochem Biophys 1993, 302: 255–258. 10.1006/abbi.1993.1207
Barthlott W, Neinhuis C: Lotusblumen und Autolacke: Ulstrastruktur, Pflanzucher, Grenzflachen und biomimetische unverschmutzbare Werkstoffe. In BIONA Report 12. Edited by: Nachtigall W, Wisser A. Gesellschaft fur Technische Biologie und Bionik, Universitat des Saarlandes; 1999:281–293.
McIntosh A, Forman M: The efficiency of the explosive discharge of the bombardier beetle with possible biomimetic application. In Design and Nature IIComparing Design in Nature with Science and Engineering. Edited by: Collins MW, Brebbia CA. Southampton & Boston: WIT Press; 2004:227–236.
Amon CH: Advances in computational modeling of nanoscale heat transfer. In Proceedings of 12th International Heat Transfer Conference. Grenoble, France; 2002:41–53.
Chen S, Doolen GD: Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 1998, 30: 329–364. 10.1146/annurev.fluid.30.1.329
Maruyama S: Molecular dynamics methods in microscale heat transfer. In Heat Transfer and Fluid Flow in Microchannels. Edited by: Celata GP. New York: Begell House Inc; 2002.
Bird GA: Molecular gas Dynamics and Direct Simulation of Gas Flows. New York: Oxford Univ. Press; 1994.
Wagner G, Flekkoy E, Fedder J, Jossang T: Coupling molecular dynamics and continuum dynamics. Comput Phys Commun 2002, 147: 670–673. 10.1016/S00104655(02)003715
Prizjev NV, Darhuber AA, Troian SM: Slip behavior in liquid films on surfaces of patterned wettability: Comparison between continuum and molecular dynamics simulations. Phys Rev E 2005, 71: 041608. 10.1103/PhysRevE.71.041608
Adkins D, Yan YY: CFD simulation of fishlike body moving in viscous liquid. J Bionic Eng 2006, 3: 147–153. 10.1016/S16726529(06)600188
Zhu Q, Wolfgang MJ, Yue DKP, Triantafyllou MS: Threedimensional flow structures and vorticity control in fishlike swimming. J Fluid Mech 2002, 468: l28. 10.1017/S002211200200143X
Rohr JJ, Hendricks EW, Quigley L, Fish FE, Gilpatrick JW, ScardinaLudwig J: Observations of dolphin swimming speed and Strouhal number. In Space and Naval Warfare Systems Center Technical Report 1769. San Diego; 1998.
Kroger R: Simulation of airflow around flapping insect wings. In Proceedings of 1st International Industrial Conference BIONIK. Hannover, Germany; 2004:185–190.
Dickinson MH, Lehmann FO, Sane SP: Science. 1999, 284: 1954–1960. 10.1126/science.284.5422.1954
Nachtigall W: BionaReport 11, Biology and Related Natural Sciences. Stuttgart: Fischer Verlag; 1997:115–156.
Zu YQ, Yan YY: Numerical simulation of electroosmotic flow near earthworm surface. J Bionic Eng 2006, 3: 179–186. 10.1016/S16726529(07)600018
Ren L, Tong J, Li J, Cheng B: Soil adhesion and biomimetics of soilengaging components: a review. J Agricult Eng 2001, 79: 239–263. 10.1006/jaer.2001.0722
Ma J: Creatures and Bionics. Tianjin: Tianjin Science and Technology Press; 1984.
Yan YY, Hull JB: The concept of electroosmotically driven flow and its application to biomimetics. J Bionic Eng 2004, 1: 46–52.
Yan YY, Ren L, Li J: The electroosmotic driven flow near an earthworm surface and the inspired bionic design in engineering. Int J Des Nat 2007, 1: 135–145. 10.2495/D&NV1N2135145
Beheshti N, Mcintosh AC: A biomimetic study of the explosive discharge of the bombardier beetle. Int J Des Nat 2007, 1: 61–69. 10.2495/D&NV1N16169
Aneshansley DJ, Eisner T: Spray aiming in the bombardier beetle: photographic evidence. Proc Natl Acad Sci USA 1999, 96: 9705–9709. 10.1073/pnas.96.17.9705
Aneshansley DJ, Eisner T, Widom M, Widom B: Biochemistry at 100°C: explosive secretory discharge of bombardier beetles (brachinus). Science 1969, 165: 61–63. 10.1126/science.165.3888.61
Dean J, Aneshansley DJ, Edgerton H, Eisner T: Defensive spray of the bombardier beetle: a biological pulse jet. Science 1990, 248: 1219–1221. 10.1126/science.2349480
Wagner G, Flekkoy E, Feder J, Jossang T: Coupling molecular dynamics and continuum dynamics. Comput Phys Commun 2002, 147: 670–673. 10.1016/S00104655(02)003715
O'Connell ST, Thompson PA: Molecular dynamicscontinuum hybrid computations: a tool for studying complex fluid flows. Phys Rev E 1995, 52: 792–795.
Priezjev NV, Darhuber AA, Troian SM: Slip behavior in liquid films on surfaces of patterned wettability: comparison between continuum and molecular dynamics simulations. Phys Rev E 2005, 71: 041608/1–041608/11. 10.1103/PhysRevE.71.041608
Qian T, Wang X: Hydrodynamic slip boundary condition at chemically patterned surfaces: a continuum deduction from molecular dynamics. Phys Rev E 2005, 72: 022501. 10.1103/PhysRevE.72.022501
Hadjiconstantinou NG: Combining atomistic and continuum simulations of contactline motion. Phys Rev E 1999, 59: 2475. 10.1103/PhysRevE.59.2475
Sousa ACM: Multiphysics modeling with SPH: from macro to nanoscale heat transfer. Proceedings of IHTC13, KN 29, Sydney, Australia 2006.
Olfe DB: A modification of the differential approximation for radiative transfer. AIAA J 1967, 5: 638–643. 10.2514/3.4041
Modest MF: The modified differential approximation for radiative transfer in general threedimensional media. J Thermophys Heat Transf 1989, 3: 283–288. 10.2514/3.28773
Asproulis N, Drikakis D: Nanoscale materials modelling using neural networks. J Comput Theoret Nanosci 2009, 6: 514–518. 10.1166/jctn.2009.1062
Wijesinghe HS, Hadjiconstantinou NG: A hybrid atomisticcontinuum formulation for unsteady, viscous, incompressible flows. CMES 2004, 5: 515–526.
Wijesinghe HS, Hornung RD, Garcia AL, Hadjiconstantinou NG: Three dimensional hybrid continuumatomistic simulations for multiscale hydrodynamics. J Fluids Eng 2004, 126: 768–777. 10.1115/1.1792275
Nie XB, Robbins MO, Chen SY: Resolving singular forces in cavity flow: multiscale modeling from atomic to millimeter scales. Phys Rev Lett 2006, 96: 1–4.
De Fabritiis G, DelgadoBuscalioni R, Coveney PV: Modeling the mesoscale with molecular specificity. Phys Rev Lett 2006, 97: 134501. 10.1103/PhysRevLett.97.134501
Schwartzentruber TE, Scalabrin LC, Boyd ID: A modular particlecontinuum numerical method for hypersonic nonequilibrium gas flows. J Comput Phys 2007, 225: 1159–1174. 10.1016/j.jcp.2007.01.022
Bhattacharya DK, Lie GC: Nonequilibrium gas flow in the transition regime: a moleculardynamics study. Phys Rev 1991, 43: 761–767. 10.1103/PhysRevA.43.761
DelgadoBuscalioni R, Coveney P: Hybrid molecularcontinuum fluid dynamics. Philos Trans R Soc Lond A 2004, 362: 1639–1654. 10.1098/rsta.2004.1401
Hadjiconstantinou NG: Discussion of recent developments in hybrid atomistic continuum methods for multiscale hydrodynamics. Bull Pol Acad Sci Tech Sci 2005, 53: 335–342.
Kalweit M, Drikakis D: Coupling strategies for hybrid molecular continuum simulation methods. Proc Inst Mech Eng C J Mech Eng Sci 2008, 222: 797–806. 10.1243/09544062JMES716
Hadjiconstantinou NG, Patera AT: Heterogeneous atomisticcontinuum representations for dense fluid systems. Int J Mod Phys 1997, 8: 967–976. 10.1142/S0129183197000837
Cao BY: Nonmaxwell slippage induced by surface roughness for microscale gas flow: a molecular dynamics simulation. Mol Phys 2007, 105: 1403–1410. 10.1080/00268970701361322
DelgadoBuscalioni R, Coveney PV: Continuumparticle hybrid coupling for mass, momentum and energy transfers. Phys Rev E 2003, 67: 046704. 10.1103/PhysRevE.67.046704
Liu J, Chen SV, Nie XB, Robbins MO: A continuumatomistic simulation of heat transfer in micro and nanoflows. J Comput Phys 2007, 227: 279–291. 10.1016/j.jcp.2007.07.014
Nie XB, Chen SY, Robbins MO: A continuum and molecular dynamics hybrid method for micro and nanofluid flow. J Fluid Mech 2004, 500: 55–64. 10.1017/S0022112003007225
Schwartzentruber TE, Scalabrin LC, Boyd ID: Hybrid particlecontinuum simulations of nonequilibrium hypersonic bluntbody flow fields. J Thermophys Heat Transf 2008, 22: 29–37. 10.2514/1.30216
Kalweit M, Drikakis D: Multiscale methods for micro/nano flows and materials. J Comput Theoret Nano Sci 2008, 5: 1923–1938. 10.1166/jctn.2008.906
Ren W, Weinan E: Heterogeneous multiscale method for the modeling of complex fluids and microfluidics. J Comput Phys 2005, 204: 1–26. 10.1016/j.jcp.2004.10.001
Schwartzentruber TE, Scalabrin LC, Boyd ID: Hybrid particlecontinuum simulations of hypersonic flow over a hollowcylinderflare geometry. AIAA J 2008, 46: 2086–2095. 10.2514/1.36681
Werder T, Walther JH, Koumoutsakos P: Hybrid atomisticcontinuum method for the simulation of dense fluid flows. J Comput Phys 2005, 205: 373–390. 10.1016/j.jcp.2004.11.019
Yan YY, Lai H, Gentle CR, Smith JM: Numerical analysis of fluid flow inside and around a liquid drop using an incorporation of multiblock iteration and moving mesh. Trans IChE Chem Eng Res Des 2002, 80: 325–331. 10.1205/026387602753582132
Drikakis D, Asproulis N: Multiscale computational modeling of flow and heat transfer. Int J Num Methods Heat Fluid Flow 2010, 20: 517–528. 10.1108/09615531011048222
Ahlborn B, Chapman S, Stafford R, Blake RW, Harper D: Experimental simulation of the thrust phases of faststart swimming of fish. J Theor Biol 1997, 200: 2301–2312.
Drucker EG, Lauder GV: Locomotor forces on a swimming fish: threedimensional vortex wake dynamics quantified using digital particle image velocimetry. J Exp Biol 1999, 202: 2393–2412.
Ahlborn B, Harper D, Blake R, Ahlborn D, Cam M: Fish without footprints. J Theor Biol 1991, 148: 521–533. 10.1016/S00225193(05)802346
Bandyopadhyay P, Castano J, Rice J, Philips R, Nedderman W, Macy W: Low speed maneuvering hydrodynamics of fish and small underwater vehicles. J Fluids Eng 1997, 119: 136–144. 10.1115/1.2819099
Cheng HK, Murillo LE: Lunatetail swimming propulsion as a problem of curved lifting line in unsteady flow. Part 1. Asymptotic theory. J Fluid Mech 1984, 143: 327–350. 10.1017/S0022112084001373
Ellington CP: The aerodynamics of hovering insect flight. V. A vortex theory. Philos Trans R Soc Lond B 1984, 305: 115–144. 10.1098/rstb.1984.0053
Dewar H, Graham J: Studies of tropical tuna swimming performance in a large water tunnelI, energetics. J Exp Biol 1994, 192: 13–31.
Dewar H, Graham J: Studies of tropical tuna swimming performance in a large water tunnelIII, kinematics. J Exp Biol 1994, 192: 45–59.
Domenici P, Blake RW: The kinematics and performance of fish faststart swimming. J Exp Biol 1997, 200: 1165–1178.
Ellington CP, van den Berg C, Thomas A: Leading edge vortices in insect flight. Nature 1996, 384: 6–26. 10.1038/384626a0
Lighthill MJ: A quatic animal propulsion of high hydromechanical efficiency. J Fluid Mech 1970, 44: 265–301. 10.1017/S0022112070001830
Lighthill MJ: Largeamplitude elongatedbody theory of fish locomotion. Proc R Soc Lond B 1971, 179: 125–138. 10.1098/rspb.1971.0085
Fish F: Power output and propulsive efficiency of swimming bottlenose dolphins. J Exp Biol 1993, 185: 179–193.
Barrett DS, Triantafyllou MS, Yue DKP, Grosenbaugh MA, Wolfgang M: Drag reduction in fishlike locomotion. J Fluid Mech 1999, 392: 183–212. 10.1017/S0022112099005455
Fish F, Hui CA: Dolphin swimminga review. Mammal Rev 1991, 21: 181–195. 10.1111/j.13652907.1991.tb00292.x
Gray J: The locomotion of nematodes. J Exp Biol 1964, 13: 135–154.
Kayan YP, Pyatetskiy VY: Kinematics of bottlenose dolphins swimming as related to acceleration mode. Bionika 1977, 11: 36–41.
Kato N: Locomotion by mechanical pectoral fins. J Mar Sci Technol 1998, 3: 113–121. 10.1007/BF02492918
Gray J: Studies in animal locomotion. VI. The propulsive powers of the dolphin. J Exp Biol 1936, 13: 192–199.
Lighthill MJ: Note on the swimming of slender fish. J Fluid Mech 1960, 9: 305–317. 10.1017/S0022112060001110
Lighthill MJ: Hydromechanics of aquatic animal propulsion. Annu Rev Fluid Mech 1969, 1: 413–445. 10.1146/annurev.fl.01.010169.002213
Liu H, Ellington CP, Kawachi K, van den Berg C, Wilmlmott AP: A computational fluid dynamic study of hawkmoth hovering. J Exp Biol 1998, 201: 461–477.
Liu H, Wassenberg R, Kawachi K: The threedimensional hydrodynamics of tadpole swimming. J Exp Biol 1997, 200: 2807–2819.
Maxworthy T: Experiments on theWeisFogh mechanism of lift generation by insects in hovering flight. Part I. Dynamics of the fling. J Fluid Mech 1979, 93: 47–63. 10.1017/S0022112079001774
Muller U, van den Heuvel B, Stamhuis E, Videler J: Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet ( Chelon labrosus risso ). J Exp Biol 1997, 200: 2893–2896.
Weihs D: The mechanism of rapid starting of slender fish. Biorheology 1973, 10: 343–350.
Wolfgang M, Anderson JM, Grosenbaugh MA, Yue DKP, Triantafyllou MS: Near body flow dynamics in swimming fish. J Exp Biol 1999, 202: 23032327.
Newman JN, Wu T: A generalized slenderbody theory for fishlike forms. J Fluid Mech 1973, 57: 673–693. 10.1017/S0022112073001953
Wu T: Hydromechanics of swimming fishes and cetaceans. Adv Appl Math 1971, 11: 1–63.
Rome L, Swank D, Corda D: How fish power swimming. Science 1993, 261: 340–343. 10.1126/science.8332898
Triantafyllou GS, Triantafyllou MS, Grosenbaugh MA: Optimal thrust development in oscillating foils with application to fish propulsion. J Fluids Struct 1993, 7: 205–224. 10.1006/jfls.1993.1012
Triantafyllou MS, Triantafyllou GS: An efficient swimming machine. Sci Am 1995, 272: 64–70. 10.1038/scientificamerican039564
Weihs D: A hydrodynamical analysis of fish turning maneuvers. Proc R Soc Lond Ser B 1972, 182: 59–72. 10.1098/rspb.1972.0066
Triantafyllou MS, Barrett DS, Yue DKP, Anderson JM, Grosenbaugh MA: A new paradigm of propulsion and maneuvering for marine vehicles. Trans Soc Naval Architects Mar Eng 1996, 104: 81–100.
Fierstine H, Walters V: Studies in locomotion and anatomy of scombroid fishes. Mem Soc South Calif Acad Sci 1968, 6: 1–31.
Videler JJ, Muller UK, Stamhuis EJ: Aquatic vertebrate locomotion: wakes from body waves. J Exp Biol 1999, 202: 3423–3430.
Kagemoto H, Wolfgang M, Yue D, Triantafyllou M: Force and power estimation in fishlike locomotion using a vortexlattice method. Trans ASME J Fluids Eng 2000, 122: 239–253. 10.1115/1.483251
Newman J: The force on a slender fishlike body. J Fluid Mech 1973, 58: 689–702. 10.1017/S0022112073002429
Lan C: The unsteady quasivortexlattice method with applications to animal propulsion. J Fluid Mech 1979, 93: 747–765. 10.1017/S0022112079002019
Triantafyllou MS, Barrett DS, Yue DKP, Anderson JM, Grosenbaugh MA, Streitlien K, Triantafyllou GS: A new paradigm of propulsion and maneuvering for marine vehicles. Trans Soc Naval Architect Mar Eng 1996, 104: 81–100.
Pedley TJ, Hill SJ: Largeamplitude undulatory fish swimming: fluid mechanics coupled to internal mechanics. J Expl Biol 1999, 202: 3431–3438.
Triantafyllou G, Triantafyllou M, Yue DKP: Hydrodynamics of fish swimming. Annu Rev Fluid Mech 2000, 32: 33–53. 10.1146/annurev.fluid.32.1.33
Liu H, Wassersug RJ, Kawachi KA: Computational fluid dynamic study of tadpole swimming. J Exp Biol 1996, 199: 1245–1260.
Cheng JY, Zhuang LX, Tong BG: Analysis of swimming threedimensional waving plates. J Fluid Mech 1991, 232: 341–355. 10.1017/S0022112091003713
Anon: Biomimetics: Strategies for Product Design Inspired by Nature. Bristol: Department of Trade and Industry; 2007.
Barthelat F, Tang H, Zavattieri PD, Li CM, Espinosa HD: On the mechanics of motherofpearl: a key feature in the material hierarchical structure. J Mech Phys Solids 2007, 55: 306–337. 10.1016/j.jmps.2006.07.007
Bhushan B, Jung YC: Wetting, adhesion and friction of superhydrophobic and hydrophilic leaves and fabricated micro/nanopatterned surfaces. J Phys Condens Matter 2008, 20: 225010. 10.1088/09538984/20/22/225010
Bhushan B, Sayer RA: Surface characterization and friction of a bioinspired reversible adhesive tape. Microsyst Technol 2007, 13: 71–78. 10.1007/s0054200602562
Elbaum R, Gorb S, Fratzl P: Structures in cell wall that enable hygroscopic movement of wheat awns. J Struct Biol 2008, 164: 101–107. 10.1016/j.jsb.2008.06.008
Gorb S, Varenberg M, Peressadko A, Tuma J: Biomimetic mushroomshaped fibrillar adhesive microstructure. J R Soc Interface 2007, 4: 271–275. 10.1098/rsif.2006.0164
Goswami L, Dunlop JWC, Jungniki K, Eder M, Gierlinger N, Coutand C, Jeronimidis G, Fratzl P, Burgert I: Stress generation in the tension wood of poplar is based on the lateral swelling power of the Glayer. Plant J 2008, 56: 531–538. 10.1111/j.1365313X.2008.03617.x
Koch K, Bhushan B, Barthlott W: Multifunctional surface structures of plants: an inspiration for biomimetics. Prog Mater Sci 2009, 54: 137–178. 10.1016/j.pmatsci.2008.07.003
Luz GM, Mano JF: Biomimetic design of materials and biomaterials inspired by the structure of nacre. Philos Trans R Soc A 2009, 367: 1587–1605. 10.1098/rsta.2009.0007
Mueller T: Biomimetics design by natures. Natl Geogr 2008, 2008: 68–90.
Reed EJ, Klumb L, Koobatian M, Viney C: Biomimicry as a route to new materials: what kinds of lessons are useful? Philos Trans R Soc A 2009, 367: 1571–1585. 10.1098/rsta.2009.0010
Stegmaier T, Linke M, Planck H: Bionics in textiles: flexible and translucent thermal insulations for solar thermal applications. Philos Trans R Soc A 2009., 367: 10.1098/rsta.2009.0019
van der Zwaag S, van Dijk N, Jonkers H, Mookhoek S, Sloof W: Self healing behaviour in manmade engineering materials: bioinspired but tasking into account their intrinsic character. Philos Trans R Soc A 2009., 367: 10.1098/rsta.2009.0020
Youngblood JP, Sottos NR: Bioinspired materials for selfcleaning and selfhealing. MRS Bull 2008, 33: 732–738. 10.1557/mrs2008.158
Yan YY: Recent advances in computational simulation of macro, meso, and microscale biomimetics related fluid flow problems. J Bionic Eng 2007, 4: 97–107. 10.1016/S16726529(07)600213
Shan X, Chen H: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 1993, 47: 1815–1819. 10.1103/PhysRevE.47.1815
Shan X, Chen H: Simulation of nonideal gases and liquidgas phase transitions by a lattice Boltzmann equation. Phys Rev E 1994, 49: 2941–2948. 10.1103/PhysRevE.49.2941
Swift MR, Osborn WR, Yeomans JM: Lattice Boltzmann simulation of nonideal fluids. Phys Rev Lett 1995, 75: 830–833. 10.1103/PhysRevLett.75.830
He XY, Chen SY, Zhang RY: A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of RayleighTaylor instability. J Comput Phys 1999, 152: 642–663. 10.1006/jcph.1999.6257
Ji CY, Yan YY: A molecular dynamics simulation of liquidvaporvaporsolid system near triplephase contact line of flow boiling in a microchannel. Appl Therm Eng 2008, 28: 195–202. 10.1016/j.applthermaleng.2007.03.029
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Saha, S.K., Celata, G.P. Advances in modelling of biomimetic fluid flow at different scales. Nanoscale Res Lett 6, 344 (2011). https://doi.org/10.1186/1556276X6344
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DOI: https://doi.org/10.1186/1556276X6344