Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Computational Methods for Unsteady Flows

  • Chapter
Unsteady Computational Fluid Dynamics in Aeronautics

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 104))

  • 4210 Accesses

Abstract

Computational methods for unsteady flows are discussed. These range from standard to modern advanced approaches. An extensive overview of temporal discretizations is given. Then adaptive time stepping approaches are outlined, including adjoint based methods. Spatial schemes are discussed, including modern higher order and resolution approaches. Numerical techniques for both density and pressure-based solvers are considered. The critical issue of numerical smoothing and its control are outlined. Also, the strong relationship between grid topology and solution accuracy is considered for a range of numerical schemes. Simultaneous equations solvers and also boundary conditions are discussed. For the latter there is a strong focus on non-reflective conditions. A survey of work suggests that even though a wide range of schemes is found, just small subsets of these find practical use.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • A. Agarwal, P.J. Morris, Direct simulation of acoustic scattering on a rotorcraft fuselage, in Proceedings of 6th AIAA/CEAS Aeroacoustics Conference, Lahaina, Hawaii, 12–14 June 2000. AIAA 2000–2030

    Google Scholar 

  • Y. Allaneau, A. Jameson, Direct numerical simulations of a two-dimensional viscous flow in a shocktube using a kinetic energy preserving scheme, in Proceedings of 19th AIAA Computational Fluid Dynamics, San Antonio, Texas, 22–25 June 2010a. AIAA 2009–3797

    Google Scholar 

  • Y. Allaneau, A. Jameson, Direct numerical simulations of plunging airfoils, in Proceedings of 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, 4–7 January 2010b. AIAA 2010–728

    Google Scholar 

  • A. Arakawa, Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I. J. Comput. Phys. 1(1), 119–143 (1966)

    MATH  Google Scholar 

  • U.M. Ascher, L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, vol. 61 (SIAM, Philadelphia, 1998)

    MATH  Google Scholar 

  • G. Ashcroft, X. Zhang, A computational investigation of the noise radiated by flow-induced cavity oscillations. AIAA Pap. 512 (2001)

    Google Scholar 

  • H.L. Atkins, D.P. Lockard, A high-order method using unstructured grids for the aeroacoustic analysis of realistic aircraft configurations. AIAA Pap. 99–1945 (1999)

    Google Scholar 

  • I.E. Barton, R. Kirby, Finite difference scheme for the solution of fluid flow problems on non-staggered grids. Int. J. Numer. Methods Fluids 33(7), 939–959 (2000)

    MathSciNet  MATH  Google Scholar 

  • R.M. Beam, R.F. Warming, An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. J. Comput. Phys. 22(1), 87–110 (1976)

    MathSciNet  MATH  Google Scholar 

  • R.M. Beam, R.F. Warming, Implicit numerical methods for the compressible Navier-Stokes and Euler equations, in Computational Fluid Dynamics. Lecture Series, vol. 1, Von Karman Institute for Fluid Dynamics, Belgium, 29 March–2 April 1982

    Google Scholar 

  • B.C. Bell, K.S. Surana, A space–time coupled p-version least-squares finite element formulation for unsteady fluid dynamics problems. Int. J. Numer. Methods Eng. 37(20), 3545–3569 (1994)

    MathSciNet  MATH  Google Scholar 

  • A. Birkefeld, C.D. Munz, Simulations of airfoil noise with the discontinuous Galerkin solver NoisSol. ERCOFTAC Bull. 90, 28–33 (2012)

    Google Scholar 

  • N.J. Bisek, D.P. Rizzetta, J. Poggie, Plasma control of a turbulent shock boundary-layer interaction. AIAA J. (2013). doi:10.2514/1.J052248

    Google Scholar 

  • G.A. Blaisdell, E.T. Spyropoulos, J.H. Qin, The effect of the formulation of nonlinear terms on aliasing errors in spectral methods. Appl. Numer. Math. 21(3), 207–219 (1996)

    MathSciNet  MATH  Google Scholar 

  • C. Bogey, C. Bailly, A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194(1), 194–214 (2004)

    MATH  Google Scholar 

  • D.L. Book, J.P. Boris, K. Hain, Flux-corrected transport II: generalizations of the method. J. Comput. Phys. 18(3), 248–283 (1975)

    MATH  Google Scholar 

  • J.P. Boris, D.L. Book, Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works. J. Comput. Phys. 11(1), 38–69 (1973)

    MATH  Google Scholar 

  • A. Brandt, Multilevel adaptive computations in fluid dynamics. AIAA J. 18(10), 1165–1172 (1980)

    MathSciNet  MATH  Google Scholar 

  • K.E. Brenan, S.L.V. Campbell, L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (SIAM, Philadelphia, 1996)

    MATH  Google Scholar 

  • W. Briley, H. McDonald, Solution of the three-dimensional compressible Navier-Stokes equations by an implicit technique, in Proceedings of the 4th International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics (Springer, Berlin, 1975), pp. 105–110

    Google Scholar 

  • T. Broeckhoven, J. Ramboer, S. Smirnov, C. Lacor, Numerical methods, in Large-Eddy Simulation for Acoustics, ed. by C. Wagner, T. Huttl, P. Sagaut (Cambridge University Press, Cambridge, 2007)

    Google Scholar 

  • J. Burmeister, G. Horton, Time-parallel multigrid solution of the Navier-Stokes equations. Multigrid Methods III 98, 155–166 (1991)

    MathSciNet  Google Scholar 

  • T.D. Butler, LINC method extensions, in Proceedings of the Second International Conference on Numerical Methods in Fluid Dynamics (Springer, Berlin, 1971), pp. 435–440

    Google Scholar 

  • M.S. Campobasso, M.B. Giles, Effects of flow instabilities on the linear analysis of turbomachinery aeroelasticity. J. Propuls. Power 19(2), 250–259 (2003)

    Google Scholar 

  • M.S. Campobasso, M.B. Giles, Stabilization of linear flow solver for turbomachinery aeroelasticity using recursive projection method. AIAA J. 42(9), 1765–1774 (2004)

    Google Scholar 

  • M. Chapman, FRAM—nonlinear damping algorithms for the continuity equation. J. Comput. Phys. 44(1), 84–103 (1981)

    MATH  Google Scholar 

  • G. Chesshire, W.D. Henshaw, Composite overlapping meshes for the solution of partial differential equations. J. Comput. Phys. 90(1), 1–64 (1990)

    MathSciNet  MATH  Google Scholar 

  • Y. Choi, C. Merkle, Time-derivative preconditioning for viscous flows, in 22nd AIAA, Fluid Dynamics, Plasma Dynamics and Lasers Conference (1991). AIAA–91–1652

    Google Scholar 

  • A.J. Chorin, A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2(1), 12–26 (1967)

    MATH  Google Scholar 

  • F.K. Chow, P. Moin, A further study of numerical errors in large-eddy simulations. J. Comput. Phys. 184(2), 366–380 (2003)

    MATH  Google Scholar 

  • Y.M. Chung, P.G. Tucker, Accuracy of higher-order finite difference schemes on nonuniform grids. AIAA J. 41(8), 1609–1611 (2003)

    Google Scholar 

  • T. Colonius, S.K. Lele, Computational aeroacoustics: progress on nonlinear problems of sound generation. Prog. Aerosp. Sci. 40(6), 345–416 (2004)

    Google Scholar 

  • W.P. Crowley, Second-order numerical advection. J. Comput. Phys. 1(4), 471–484 (1967)

    MATH  Google Scholar 

  • F. Daude, J. Berland, T. Emmert, P. Lafon, F. Crouzet, C. Bailly, A high-order finite-difference algorithm for direct computation of aerodynamic sound. Comput. Fluids 61, 46–63 (2012)

    MathSciNet  Google Scholar 

  • R.W. Davis, E.F. Moore, A numerical study of vortex shedding from rectangles. J. Fluid Mech. 116(3), 475–506 (1982)

    MATH  Google Scholar 

  • C.C. de Wiart, K. Hillewaert, P. Geuzaine, DNS of a low pressure turbine blade computed with the discontinuous Galerkin method, in Proceedings of the ASME Turbo Expo, Copenhagen, Denmark, 11–15 June 2012. GT2012–68900

    Google Scholar 

  • J.W. Deardorff, A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41(02), 453–480 (1970)

    MATH  Google Scholar 

  • I. Demirdžić, M. Perić, Space conservation law in finite volume calculations of fluid flow. Int. J. Numer. Methods Fluids 8(9), 1037–1050 (1988)

    MATH  Google Scholar 

  • J. Douglas, J.E. Gunn, A general formulation of alternating direction methods. Numer. Math. 6(1), 428–453 (1964)

    MathSciNet  MATH  Google Scholar 

  • D. Drikakis, W. Rider, High-Resolution Methods for Incompressible and Low-Speed Flows (Springer, Berlin, 2004)

    Google Scholar 

  • F. Ducros, V. Ferrand, F. Nicoud, C. Weber, D. Darracq, C. Gacherieu, T. Poinsot, Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys. 152(2), 517–549 (1999)

    MATH  Google Scholar 

  • F. Ducros, F. Laporte, T. Souleres, V. Guinot, P. Moinat, B. Caruelle, High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows. J. Comput. Phys. 161(1), 114–139 (2000)

    MathSciNet  MATH  Google Scholar 

  • J.K. Dukowicz, J.D. Ramshaw, Tensor viscosity method for convection in numerical fluid dynamics. J. Comput. Phys. 32(1), 71–79 (1979)

    MATH  Google Scholar 

  • M.S. Engelman, R.L. Sani, Finite element simulation of incompressible fluid flows with a free/moving surface. Comput. Tech. Fluid. Flow 47, 47–74 (1986)

    MathSciNet  Google Scholar 

  • C.A.J. Fletcher, Fundamental and General Techniques. Computational Techniques for Fluid Dynamics, vol. 1 (Springer, Berlin, 1997)

    Google Scholar 

  • G. Fritsch, M. Giles, Second-order effects of unsteadiness on the performance of turbomachines, in 37th International Gas Turbine and Aeroengine Congress and Exposition (1992). GT–92–389

    Google Scholar 

  • L. Gamet, F. Ducros, F. Nicoud, T. Poinsot, Compact finite difference schemes on non-uniform meshes. application to direct numerical simulations of compressible flows. Int. J. Numer. Methods Fluids 29(2), 159–191 (1999)

    MathSciNet  MATH  Google Scholar 

  • B.J. Geurts, D.D. Holm, Regularization modeling for large-eddy simulation. Phys. Fluids 15(1), L13–L16 (2003)

    MathSciNet  Google Scholar 

  • S. Ghosal, An analysis of numerical errors in large-eddy simulations of turbulence. J. Comput. Phys. 125(1), 187–206 (1996)

    MathSciNet  MATH  Google Scholar 

  • M.B. Giles, Nonreflecting boundary conditions for Euler equation calculations. AIAA J. 28(12), 2050–2058 (1990)

    Google Scholar 

  • M. Giles, The HYDRA user’s guide. Version 0.06 (2004)

    Google Scholar 

  • W. Glanfield, Personal communication (2000)

    Google Scholar 

  • J. Glass, W. Rodi, A higher order numerical scheme for scalar transport. Comput. Methods Appl. Mech. Eng. 31(3), 337–358 (1982)

    MATH  Google Scholar 

  • P.M. Gresho, R.L. Lee, R.L. Sani, On the time-dependent solution of the incompressible Navier-Stokes equations in two and three dimensions. Recent Adv. Numer. Methods Fluids 1, 27–79 (1980)

    Google Scholar 

  • P.M. Gresho, S.T. Chan, R.L. Lee, C.D. Upson, A modified finite element method for solving the time-dependent, incompressible Navier-Stokes equations. Part 1: theory. Int. J. Numer. Methods Fluids 4(6), 557–598 (1984)

    MATH  Google Scholar 

  • A. Hadjadj, Large eddy simulation of shock/boundary layer interaction. AIAA J. 50(12), 2919–2927 (2012)

    Google Scholar 

  • T. Haga, H. Gao, Z.J. Wang, A high-order unifying discontinuous formulation for the Navier-Stokes equations on 3d mixed grids. Math. Model. Nat. Phenom. 6(3), 28–56 (2011)

    MathSciNet  MATH  Google Scholar 

  • F.H. Harlow, J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189 (1965)

    MATH  Google Scholar 

  • A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49(3), 357–393 (1983)

    MathSciNet  MATH  Google Scholar 

  • A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys. 71(2), 231–303 (1987)

    MathSciNet  MATH  Google Scholar 

  • L. He, D.X. Wang, Concurrent blade aerodynamic-aero-elastic design optimization using adjoint method. J. Turbomach. 133, 011021 (2011)

    Google Scholar 

  • L.S. Hedges, A.K. Travin, P.R. Spalart, Detached-eddy simulations over a simplified landing gear. J. Fluids Eng. 124(2), 413–423 (2002)

    Google Scholar 

  • R.A.W.M. Henkes, Natural-convection boundary layers. PhD thesis, Technical University Delft (1990)

    Google Scholar 

  • B.P. Hignett, A.A. White, R.D. Carter, W.D.N. Jackson, R.M. Small, A comparison of laboratory measurements and numerical simulations of baroclinic wave flows in a rotating cylindrical annulus. Q. J. R. Meteorol. Soc. 111(467), 131–154 (1985)

    Google Scholar 

  • C.W. Hirt, A.A. Amsden, J.L. Cook, An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14(3), 227–253 (1974)

    MATH  Google Scholar 

  • R. Hixon, Prefactored small-stencil compact schemes. J. Comput. Phys. 165(2), 522–541 (2000)

    MathSciNet  MATH  Google Scholar 

  • K. Horiuti, T. Itami, Truncation error analysis of the rotational form for the convective terms in the Navier–Stokes equation. J. Comput. Phys. 145(2), 671–692 (1998)

    MATH  Google Scholar 

  • F.Q. Hu, A stable, perfectly matched layer for linearized Euler equations in unsplit physical variables. J. Comput. Phys. 173(2), 455–480 (2001)

    MathSciNet  MATH  Google Scholar 

  • F.Q. Hu, M.Y. Hussaini, J.L. Manthey, Low-dissipation and low-dispersion Runge–Kutta schemes for computational acoustics. J. Comput. Phys. 124(1), 177–191 (1996)

    MathSciNet  MATH  Google Scholar 

  • A. Hujeirat, R. Rannacher, A method for computing compressible, highly stratified flows in astrophysics based on operator splitting. Int. J. Numer. Methods Fluids 28(1), 1–22 (1998)

    MathSciNet  MATH  Google Scholar 

  • H.G. Im, Numerical studies of transient opposed-flow flames using adaptive time integration. KSME Int. J. 14(1), 103–112 (2000)

    Google Scholar 

  • A. Iserles, Generalized leapfrog methods. IMA J. Numer. Anal. 6(4), 381–392 (1986)

    MathSciNet  MATH  Google Scholar 

  • R.I. Issa, Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62(1), 40–65 (1986)

    MathSciNet  MATH  Google Scholar 

  • A. Jameson, Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings. AIAA Pap. 1596, 1991 (1991)

    Google Scholar 

  • A. Jameson, The construction of discretely conservative finite volume schemes that also globally conserve energy or entropy. J. Sci. Comput. 34(2), 152–187 (2008a)

    MathSciNet  MATH  Google Scholar 

  • A. Jameson, Formulation of kinetic energy preserving conservative schemes for gas dynamics and direct numerical simulation of one-dimensional viscous compressible flow in a shock tube using entropy and kinetic energy preserving schemes. J. Sci. Comput. 34(2), 188–208 (2008b)

    MathSciNet  MATH  Google Scholar 

  • A. Jameson, W. Schmidt, E. Turkel, Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA Pap. 81(125), 9 (1981)

    Google Scholar 

  • R.J. Jefferson-Loveday, Numerical simulations of unsteady impinging jet flows. PhD thesis, Swansea University (2008)

    Google Scholar 

  • W.P. Jones, A.J. Marquis, Calculation of axisymmetric re-circulating flows with a second order turbulence model, in Proc. of the 5th Symp. on Turbulent Shear Flows, Cornel University (1985), pp. 20.1–20.11

    Google Scholar 

  • J. Joo, P. Durbin, Simulation of turbine blade trailing edge cooling. J. Fluids Eng. 131, 021102 (2009)

    Google Scholar 

  • S.A. Karabasov, V.M. Goloviznin, New efficient high-resolution method for nonlinear problems in aeroacoustics. AIAA J. 45(12), 2861–2871 (2007)

    Google Scholar 

  • S.A. Karabasov, V.M. Goloviznin, Compact accurately boundary-adjusting high-resolution technique for fluid dynamics. J. Comput. Phys. 228(19), 7426–7451 (2009)

    MathSciNet  MATH  Google Scholar 

  • Z. Khatir, Discrete vortex modelling of near-wall flow structure in turbulent boundary layers. PhD thesis, Fluid Dynamics Research Centre, The University of Warwick (2000)

    Google Scholar 

  • J.W. Kim, D.J. Lee, Optimized compact finite difference schemes with maximum resolution. AIAA J. 34(5), 887–893 (1996)

    MATH  Google Scholar 

  • J. Kim, P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59(2), 308–323 (1985)

    MathSciNet  MATH  Google Scholar 

  • M.H. Kobayashi, J.C.F. Pereira, Culation of incompressible laminar flows on a nonstaggered, nonorthogonal grid. Numer. Heat Transf., Part B, Fundam. 19(2), 243–262 (1991)

    Google Scholar 

  • J.A. Krakos, D.L. Darmofal, Effect of small-scale output unsteadiness on adjoint-based sensitivity. AIAA J. 48(11), 2611–2623 (2010)

    Google Scholar 

  • C. Lacor, Industrial Computational Fluid Dynamics. Lecture Series 1999-06 (von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, 1999)

    Google Scholar 

  • S. Laizet, E. Lamballais, High-order compact schemes for incompressible flows: a simple and efficient method with quasi-spectral accuracy. J. Comput. Phys. 228(16), 5989–6015 (2009)

    MathSciNet  MATH  Google Scholar 

  • K.R. Lee, J.H. Park, K.H. Kim, High-order interpolation method for overset grid based on finite volume method. AIAA J. 49(7), 1387–1398 (2011)

    Google Scholar 

  • C.E. Leith, Numerical simulation of the earth’s atmosphere. University of California, Lawrence Radiation Laboratory (1964)

    Google Scholar 

  • S.K. Lele, Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103(1), 16–42 (1992)

    MathSciNet  MATH  Google Scholar 

  • B.P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19(1), 59–98 (1979)

    MATH  Google Scholar 

  • M.S. Liou, C.J. Steffen, A new flux splitting scheme. J. Comput. Phys. 107(1), 23–39 (1993)

    MathSciNet  MATH  Google Scholar 

  • X.D. Liu, S. Osher, T. Chan, Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115(1), 200–212 (1994)

    MathSciNet  MATH  Google Scholar 

  • Y. Liu, M. Vinokur, Z.J. Wang, Spectral (finite) volume method for conservation laws on unstructured grids v: extension to three-dimensional systems. J. Comput. Phys. 212(2), 454–472 (2006)

    MathSciNet  MATH  Google Scholar 

  • D.P. Lockard, K.S. Brentner, H.L. Atkins, High-accuracy algorithms for computational aeroacoustics. AIAA J. 33, 246–251 (1995)

    MATH  Google Scholar 

  • S. Loiodice, P.G. Tucker, J. Watson, Coupled open rotor engine intake simulations, in Proceedings of the 48th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, Florida, 4–7 January 2010. AIAA 2010–840

    Google Scholar 

  • Y. Lu, W.N. Dawes, X. Yuan, Investigation of 3D internal flow using new flux-reconstruction higher order method, in Proceedings of the ASME Turbo Expo, Copenhagen, Denmark, 11–15 June 2012. GT2012–69270

    Google Scholar 

  • K. Mani, D.J. Mavriplis, Discrete adjoint based time-step adaptation and error reduction in unsteady flow problems, in 18th AIAA Computational Fluid Dynamics Conference, Miami, FL, 25–28 June 2007. AIAA 2007–3944

    Google Scholar 

  • K. Mani, D.J. Mavriplis, Spatially non-uniform time-step adaptation for functional outputs in unsteady flow problems, in 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, 4–7 January 2010. AIAA 2010–121

    Google Scholar 

  • E. Manoha, B. Troff, P. Sagaut, Trailing-edge noise prediction using large-eddy simulation and acoustic analogy. AIAA J. 38(4), 575–583 (2000)

    Google Scholar 

  • J.C. Marongiu, F. Leboeuf, E. Parkinson, Numerical simulation of the flow in a Pelton turbine using the meshless method smoothed particle hydrodynamics: a new simple solid boundary treatment. Proc. Inst. Mech. Eng. A, J. Power Energy 221(6), 849–856 (2007)

    Google Scholar 

  • J.C. Marongiu, F. Leboeuf, J.Ë. Caro, E. Parkinson, Free surface flows simulations in Pelton turbines using an hybrid SPH-ALE method. J. Hydraul. Res. 48(S1), 40–49 (2010)

    Google Scholar 

  • I. Mary, P. Sagaut, Large eddy simulation of flow around an airfoil near stall. AIAA J. 40(6), 1139–1145 (2002)

    Google Scholar 

  • P.J. Morris, L.N. Long, A. Bangalore, Q. Wang, A parallel three-dimensional computational aeroacoustics method using nonlinear disturbance equations. J. Comput. Phys. 133(1), 56–74 (1997)

    MATH  Google Scholar 

  • C. Moulinec, S. Benhamadouche, D. Laurence, M. Peric, LES in a U-bend pipe meshed by polyhedral cells. Eng. Turbul. Model. Exp. 6, 237–246 (2005)

    Google Scholar 

  • B. Muhlbauer, B. Noll, M. Aigner, Numerical investigation of entropy noise and its acoustic sources in aero-engine, in Proceedings of the ASME Turbo Expo, Berlin, Germany, 9–13 June 2008. GT2008–50321

    Google Scholar 

  • T. Muramatsu, H. Ninokata, Thermal striping temperature fluctuation analysis using the algebraic stress turbulence model in water and sodium. JSME Int. J., Ser. 2, Fluids Eng. Heat Transf. Power Combust. Thermophys. Prop. 35(4), 486–496 (1992)

    Google Scholar 

  • K. Nakahashi, F. Togashi, Unstructured overset grid method for flow simulation of complex multiple body problems, in ICAS 2000 Congress, (2000). ICAS 0263

    Google Scholar 

  • A.G.F.A. Nasser, M.A. Leschziner, Computation of transient recirculating flow using spline approximations and time-space characteristics, in Proc. 4th Int. Conf. on Numerical Methods in Laminar and Turbulent Flow, Swansea (1985), pp. 480–491

    Google Scholar 

  • P.D. Orkwis, M.G. Turner, J.W. Barter, Linear deterministic source terms for hot streak simulations. J. Propuls. Power 18(2), 383–389 (2002)

    Google Scholar 

  • S.A. Orszag, Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50(4), 689–703 (1971)

    MATH  Google Scholar 

  • Y. Ozyoruk, L.N. Long, Multigrid acceleration of a high-resolution computational aeroacoustics scheme. AIAA J. 35(3), 428–433 (1997)

    Google Scholar 

  • U. Paliath, H. Shen, R. Avancha, C. Shieh, Large eddy simulation for jets from chevron and dual nozzles, in Proceedings of 17th AIAA/CEAS Aeroacoustics Conference, Portland, Oregon, 5–8 June 2011. AIAA 2011–2881

    Google Scholar 

  • A.T. Patera, A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54(3), 468–488 (1984)

    MathSciNet  MATH  Google Scholar 

  • L.L. Pauley, P. Moin, W.C. Reynolds, The structure of two-dimensional separation. J. Fluid Mech. 220(1), 397–411 (1990)

    Google Scholar 

  • D.W. Peaceman, H.H. Rachford, The numerical solution of parabolic and elliptic differential equations. J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955)

    MathSciNet  MATH  Google Scholar 

  • A. Pinelli, I.Z. Naqavi, U. Piomelli, J. Favier, Immersed-boundary methods for general finite-difference and finite-volume Navier–Stokes solvers. J. Comput. Phys. 229(24), 9073–9091 (2010)

    MathSciNet  MATH  Google Scholar 

  • H. Pitsch, Large-eddy simulation of turbulent combustion. Annu. Rev. Fluid Mech. 38, 453–482 (2006)

    MathSciNet  Google Scholar 

  • W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes: The Art of Scientific Computing (FORTRAN) (Cambridge University Press, Cambridge, 1989)

    MATH  Google Scholar 

  • D. Rayner, A numerical study into the heat transfer beneath the stator blade of an axial compressor. PhD thesis, School of Engineering, University of Sussex (1993)

    Google Scholar 

  • D.T. Reindl, W.A. Beckman, J.W. Mitchell, C.J. Rutland, Benchmarking transient natural convection in an enclosure, in National Heat Transfer Conference, vol. 91 (1991), pp. 1–7

    Google Scholar 

  • C.M. Rhie, W.L. Chow, Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21(11), 1525–1532 (1983)

    MATH  Google Scholar 

  • D.P. Rizzetta, M.R. Visbal, P.E. Morgan, A high-order compact finite-difference scheme for large-eddy simulation of active flow control. Prog. Aerosp. Sci. 44(6), 397–426 (2008)

    Google Scholar 

  • P.J. Roache, A flux-based modified method of characteristics. Int. J. Numer. Methods Fluids 15(11), 1259–1275 (1992)

    MathSciNet  MATH  Google Scholar 

  • P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43(2), 357–372 (1981)

    MathSciNet  MATH  Google Scholar 

  • P.L. Roe, Characteristic-based schemes for the Euler equations. Annu. Rev. Fluid Mech. 18(1), 337–365 (1986)

    MathSciNet  Google Scholar 

  • S.E. Rogers, D. Kwak, Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations. AIAA J. 28, 253–262 (1990)

    MATH  Google Scholar 

  • S.E. Rogers, D. Kwak, J.L.C. Chang, Numerical solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. NASA STI/Recon Tech. Rep. N 87, 11964 (1986)

    Google Scholar 

  • M.P. Rumpfkeil, D.W. Zingg, A general framework for the optimal control of unsteady flows with applications, in Proceedings of the 45th AIAA Aerospace Meeting and Exhibit. Reno, Nevada, 8–11 January 2007. AIAA 2010–1128

    Google Scholar 

  • N.D. Sandham, Q. Li, H.C. Yee, Entropy splitting for high-order numerical simulation of compressible turbulence. J. Comput. Phys. 178(2), 307–322 (2002)

    MATH  Google Scholar 

  • L.J. Segerlind, Applied Finite Element Analysis (Wiley, New York, 1976)

    MATH  Google Scholar 

  • V. Seidl, M. Peric, M. Schmidt, Space-and time-parallel Navier-Stokes solver for 3d block-adaptive Cartesian grids, in Proceedings of the Parallel Computational Fluid Dynamics, vol. 95 (1995), pp. 557–584

    Google Scholar 

  • J.A. Sethian, Fast marching methods. SIAM Rev. 41(2), 199–235 (1999)

    MathSciNet  MATH  Google Scholar 

  • M.L. Shur, P.R. Spalart, M.K. Strelets, A.K. Travin, Towards the prediction of noise from jet engines. Int. J. Heat Fluid Flow 24(4), 551–561 (2003)

    Google Scholar 

  • S. Skelboe, The control of order and steplength for backward differentiation methods. BIT Numer. Math. 17(1), 91–107 (1977)

    MathSciNet  MATH  Google Scholar 

  • P. Spalart, L. Hedges, M. Shur, A. Travin, Simulation of active flow control on a stalled airfoil. Flow Turbul. Combust. 71(1), 361–373 (2003)

    MATH  Google Scholar 

  • E.T. Spyropoulos, G.A. Blaisdell, Large-eddy simulation of a spatially evolving supersonic turbulent boundary-layer flow. AIAA J. 36(11), 1983–1990 (1998)

    Google Scholar 

  • D. Stanescu, M.Y. Hussaini, F. Farassat, Aircraft engine noise scattering—a discontinuous spectral element approach. AIAA Pap. 800, 2002 (2002)

    Google Scholar 

  • A. Staniforth, J. Côté, Semi-Lagrangian integration schemes for atmospheric models—a review. Mon. Weather Rev. 119(9), 2206–2223 (1991)

    Google Scholar 

  • J.L. Steger, P. Kutler, Implicit finite-difference procedures for the computation of vortex wakes. AIAA J. 15(4), 581–590 (1977)

    MathSciNet  MATH  Google Scholar 

  • J.L. Steger, R.F. Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. J. Comput. Phys. 40(2), 263–293 (1981)

    MathSciNet  MATH  Google Scholar 

  • J. Steinhoff, D. Underhill, Modification of the Euler equations for “vorticity confinement”: application to the computation of interacting vortex rings. Phys. Fluids 6, 2738–2744 (1994)

    MATH  Google Scholar 

  • M. Strelets, Detached eddy simulation of massively separated flows, in Proceedings of 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 8–11 January 2001. AIAA 2001–0879

    Google Scholar 

  • R.C. Swanson, E. Turkel, On central-difference and upwind schemes. J. Comput. Phys. 101(2), 292–306 (1992)

    MathSciNet  MATH  Google Scholar 

  • T. Talha, A numerical investigation of three-dimensional unsteady turbulent channel flow subjected to temporal acceleration. PhD thesis, School of Engineering, University of Warwick (2012)

    Google Scholar 

  • C.K.W. Tam, Advances in numerical boundary conditions for computational aeroacoustics. J. Comput. Acoust. 6(4), 377–402 (1998)

    Google Scholar 

  • C.K.W. Tam, H. Shen, Direct computation of nonlinear acoustic pulses using high order finite difference schemes. AIAA Pap. 4325 (1993)

    Google Scholar 

  • C.K.W. Tam, J.C. Webb, Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comput. Phys. 107(2), 262–281 (1993)

    MathSciNet  MATH  Google Scholar 

  • C.K.W. Tam, C. Jay, D. Zhong, A study of the short wave components in computational acoustics. J. Comput. Acoust. 1(01), 1–30 (1993)

    MathSciNet  Google Scholar 

  • L. Tang, J.D. Baeder, Uniformly accurate finite difference schemes for p-refinement. SIAM J. Sci. Comput. 20(3), 1115–1131 (1998)

    MathSciNet  Google Scholar 

  • P.D. Thomas, C.K. Lombard, Geometric conservation law and its application to flow computations on moving grids. AIAA J. 17, 1030–1037 (1979)

    MathSciNet  MATH  Google Scholar 

  • C. Tu, M. Deville, L. Dheur, L. Vanderschuren, Finite element simulation of pulsatile flow through arterial stenosis. J. Biomech. 25(10), 1141–1152 (1992)

    Google Scholar 

  • P.G. Tucker, Numerical precision and dissipation errors in rotating flows. Int. J. Numer. Methods Heat Fluid Flow 7(7), 647–658 (1997)

    MATH  Google Scholar 

  • P.G. Tucker, Computation of Unsteady Internal Flows: Fundamental Methods with Case Studies (Kluwer Academic, Dordrecht, 2001)

    Google Scholar 

  • P.G. Tucker, Novel multigrid orientated solution adaptive time-step approaches. Int. J. Numer. Methods Fluids 40(3–4), 507–519 (2002a)

    MATH  Google Scholar 

  • P.G. Tucker, Temporal behavior of flow in rotating cavities. Numer. Heat Transf., Part A, Appl. 41(6–7), 611–627 (2002b)

    Google Scholar 

  • P.G. Tucker, Novel MILES computations for jet flows and noise. Int. J. Heat Fluid Flow 25(4), 625–635 (2004)

    Google Scholar 

  • P.G. Tucker, Turbulence modelling of problem aerospace flows. Int. J. Numer. Methods Fluids 51(3), 261–283 (2006)

    MATH  Google Scholar 

  • P.G. Tucker, The LES model’s role in jet noise. Prog. Aerosp. Sci. 44(6), 427–436 (2008)

    Google Scholar 

  • A. Uzun, M.Y. Hussaini, Simulation of noise generation in near-nozzle region of a chevron nozzle jet. AIAA J. 47(8), 1793–1810 (2009)

    Google Scholar 

  • G.D. Van Albada, B. Van Leer, W.W. Roberts Jr., A comparative study of computational methods in cosmic gas dynamics. Astron. Astrophys. 108, 76–84 (1982)

    MATH  Google Scholar 

  • B. Van Leer, Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow. J. Comput. Phys. 23(3), 263–275 (1977)

    MATH  Google Scholar 

  • B. Van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32(1), 101–136 (1979)

    Google Scholar 

  • B.C. Vermeire, J.S. Cagnone, S. Nadarajah, Iles using the correction procedure via reconstruction scheme, in Proceedings of 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Grapevine, Dallas/Ft. Worth Region, Texas, 7–10 January 2013. AIAA 2013–1001

    Google Scholar 

  • M.R. Visbal, D.V. Gaitonde, On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J. Comput. Phys. 181(1), 155–185 (2002)

    MathSciNet  MATH  Google Scholar 

  • S.G. Wallis, J.R. Manson, Accurate numerical simulation of advection using large time steps. Int. J. Numer. Methods Fluids 24(2), 127–139 (1997)

    MATH  Google Scholar 

  • Z.J. Wang, Y. Liu, G. May, A. Jameson, Spectral difference method for unstructured grids ii: extension to the Euler equations. J. Sci. Comput. 32(1), 45–71 (2007)

    MathSciNet  MATH  Google Scholar 

  • J.M. Weiss, W.A. Smith, Preconditioning applied to variable and constant density flows. AIAA J. 33(11), 2050–2057 (1995)

    MATH  Google Scholar 

  • G. Yang, D.M. Causon, D.M. Ingram, R. Saunders, P. Batten, A Cartesian cut cell method for compressible flows. Part B: moving body problems. Aeronaut. J. 101(1002), 57–65 (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering, Whittle Laboratory, University of Cambridge, Cambridge, UK

    P. G. Tucker

Authors
  1. P. G. Tucker
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Tucker, P.G. (2014). Computational Methods for Unsteady Flows. In: Unsteady Computational Fluid Dynamics in Aeronautics. Fluid Mechanics and Its Applications, vol 104. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7049-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-7049-2_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7048-5

  • Online ISBN: 978-94-007-7049-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation