Smoothed particle hydrodynamics. A meshfree particle method.

*(English)*Zbl 1046.76001
River Edge, NJ: World Scientific (ISBN 981-238-456-1/hbk). xx, 449 p. £ 69.00 (2003).

The next generation of computational methods, namely the meshfree methods – based on the theory of distributions, are expected in many applications to be superior to the methods based on conventional grids (finite difference, finite element or finite volume methods). The book is focused on one of these meshfree methods, namely on the smoothed particle hydrodynamics (SPH) method. It is written for postgraduate students, researchers and professionals in both applied mathematics and engineering.

The foundations of the SPH method (the kernel approximation in continuous form and particle approximation in discretized form) are presented together with systematically derived consistency conditions. A discontinuous SPH formulation is also presented in order to simulate the discontinuous phenomena such as shock waves. In numerical techniques, some treatments such as artificial viscosity, artificial heat, variable smoothing length, choice of the time step are addressed for enhancing the stability of the computational process and to assure the accuracy of results. Many interesting and practical examples are also sketched (a detailed presentation of all the involved steps would be appropriate). These include incompressible flows, free surface flows, high-explosive detonation and explosion, underwater explosion, high-velocity impact etc. Source codes in Fortran 77 and Fortran 90 for three-dimensional Navier Stokes equations are provided with detailed descriptions.

Numerical simulations using the SPH method are a new area of research, and are still under development. These problems offer ample opportunities for researchers to develop more advanced methods as next generation numerical methods. The book can serve for a good start to efficiently learn, test, practise and develop such new methods.

The foundations of the SPH method (the kernel approximation in continuous form and particle approximation in discretized form) are presented together with systematically derived consistency conditions. A discontinuous SPH formulation is also presented in order to simulate the discontinuous phenomena such as shock waves. In numerical techniques, some treatments such as artificial viscosity, artificial heat, variable smoothing length, choice of the time step are addressed for enhancing the stability of the computational process and to assure the accuracy of results. Many interesting and practical examples are also sketched (a detailed presentation of all the involved steps would be appropriate). These include incompressible flows, free surface flows, high-explosive detonation and explosion, underwater explosion, high-velocity impact etc. Source codes in Fortran 77 and Fortran 90 for three-dimensional Navier Stokes equations are provided with detailed descriptions.

Numerical simulations using the SPH method are a new area of research, and are still under development. These problems offer ample opportunities for researchers to develop more advanced methods as next generation numerical methods. The book can serve for a good start to efficiently learn, test, practise and develop such new methods.

Reviewer: Titus Petrila (Cluj-Napoca)

##### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76M28 | Particle methods and lattice-gas methods |