The Smoothed Particle Hydrodynamics Method (SPH): Recent advances and science and engineering applications

Jaime Klapp
ABACUS-Cinvestav; ININ, Mexico

Abstract: The Smoothed Particle Hydrodynamics method (SPH) has been strengthening over the past three decades. A description of the evolution of the SPH method during this period of time is presented. Recent results that we have obtained in relation to the consistency of the method are described that has led to a reformulation of the method that allows to obtain realistic physical solutions. I describe some examples of the application of the new formalism that generates quite different solutions when compared to those obtained with the traditional formalism. The SPH applications that are presented range from astrophysics to multiphase flow through a porous media.

About the speaker: Jaime Klapp studied Physics in the National University of México (UNAM), a M. Sc. in Applied Mathematics and Theoretical Physics in Cambridge University, England and a Ph. D. in Theoretical Astrophysics in Oxford University, England. Then he did postdocs in Los Alamos National Laboratory, New Mexico, USA and the University of Florida, USA. He has done several long term visits in several countries, USA, England, Italy, Germany, Australia and Venezuela, and given lectures in many countries. He has published 12 review papers, over 150 papers (in journals and conference proceedings) and edited 13 books, most with Springer-Verlag.

He is the Head of the Computational Fluid Dynamics group of the Instituto Nacional de Investigaciones Nucleares, and he collaborated in founding the Cinvestav-Abacus Centre for Applied Mathematics and High Performance Computer where he is the head of several research projects.

He has received the Mexico State Science Award. His research focused in Astrophysical Fluid Dynamics and Computational Fluid Dynamics in general. He was the first to perform a detailed numerical study of the so-called very massive population III stars (first stars) that initially were thought did not exist, but have become quite popular in recent years. He did a very successful model of Cepheid non-linear oscillations to explain several features of the Bump Cepheids. He has devoted a large effort to understand the very complex star formation problem, with many important contributions. For doing this, he also made significant contributions in numerical methods, for solving the Jeans instability problem and more recently to produce a mathematical consistent SPH formulation that avoids unphysical results with very important implications to SPH simulations in general. He has done research in several problems related to galaxy dynamics and collisions, stellar evolution and cosmology. Other relevant numerical methods he has develop are an SPH simulation for time-dependent Poiseuille flow for low Reynolds numbers, an SPH shock-capturing SPH scheme based on adaptive kernel estimation, and new formulations for modeling the diffuse interface coexistence in equilibrium drops and a model of explosive boiling of liquid drops in microgravity, that includes a proper formulation of tension forces. With this technology he has develop with his collaborators a mathematical consistent SPH multiphase code that properly handles the interphase between two fluids. He has recently moved to new applications such as hemodynamic simulations of brain arteriovenous malformations, simulations of fractured oil reservoirs and dispersion of contaminants in soil, water and air, among others.
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