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Review of Smooth Particle Hydrodynamics and its Applications for Environmental Flows

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Journal of The Institution of Engineers (India): Series A Aims and scope Submit manuscript

Abstract

With the advancement of the computing facilities, meshless techniques have become a new arena of research for the computational scientists. Smooth particle hydrodynamics (SPH), a popular mesh free method, has shown significant potential in the numerical reproduction of many complex problems associated with environmental hydraulics. The present paper is a review of SPH approach and how it has been successfully implemented in understanding the flow physics associated with natural flow regimes. The manuscript is arranged into five sections. The first and the second sections describe the philosophy behind the development of SPH. The flow physics associated with the interaction of the solid particles and the fluid medium is explained in the third section. The next section is dedicated to the application of SPH in modelling environmental flows at different scales followed by a closure section.

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Abbreviations

\({\varvec{x}},\user2{ x^{\prime}}\) :

Position of a point

\(\delta ({\text{x}} - {\text{x}}^{^{\prime}} )\) :

Dirac delta function

W :

Smoothing function

h :

Smoothing length (L)

h 0 :

Initial smoothing length (L)

\(f({\varvec{x}})\) :

Function of position vector x

 < f(x) > :

Kernel approximated value of function f(x)

D :

Support domain

\({\alpha }_{D}\) :

Normalization constant

q :

Parameter equal to \(\frac{{\left| {{\text{x}} - {\text{x}}^{^{\prime}} ,\,h} \right|}}{h}\)

g(q):

A function of the parameter q

k :

Scaling factor

i, j :

Indices denoting the position of the particles

Re :

Remainder term

\(\nabla\) :

Delta operator

M, N,:

Total number of particles inside the support domain of the particle i

f i :

Function value at the location of a particle i

f j :

Function value at the location of a particle j

m :

Mass of the particles (M)

\(\rho\) :

Density (ML− 3)

\({\rho }_{0}\) :

Initial density (ML− 3)

n :

Exponent

t :

Time (T)

\(\Delta t\) :

Incremental time (T)

\({\varvec{V}}\) :

Velocity field (LT− 1)

\(\mu\) :

Viscosity (ML− 1 T− 1)

F external :

External force (MLT− 2)

P :

Pressure (ML− 1 T− 2)

P mod :

Modified Pressure (ML− 1 T− 2)

\({\varvec{g}}\) :

Acceleration due to gravity (LT− 2)

n d :

Number of dimensions

H avg :

Average height of the sediment stack (L)

θ :

Angle of inclination

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Acknowledgements

This work was carried out as part of the Institute Scheme for Innovative Research and Development (ISIRD) project from IIT Kharagpur.

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  1. Department of Civil Engineering, Indian Institute of Technology (IIT), Kharagpur, India

    Subhrangshu Purkayastha

  2. IIT, Kharagpur, India

    Mohammad Saud Afzal

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Purkayastha, S., Afzal, M.S. Review of Smooth Particle Hydrodynamics and its Applications for Environmental Flows. J. Inst. Eng. India Ser. A 103, 921–941 (2022). https://doi.org/10.1007/s40030-022-00650-4

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