Computational Algorithms for Multiphase Hydrodynamics Models and Filtration

Abstract

Computational algorithms for modeling of multiphase hydrodynamics processes with take of phase transitions will be discussed. The algorithms are based on discretization of conservation laws for mass, momentum, and energy in integral and differential forms. The time and spatial discretization is natural and numerical simulations are realized as direct computer experiments. The experiments are implemented as a computer simulation of the dynamics of a multiphase carrier fluid containing particles that can undergo, for example, graphite–diamond phase transitions and calculations are given. Modification of the algorithms have also been developed to take into account the influence of viscosity when simulating the dynamics of a multiphase fluid in porous media.

Computational Fluid Mechanics with Phase Transitions by Particle Methods

“…For the problems of diffusion and elasticity dynamics in heterogeneous composite media, there is a rigorous mathematical approach leading to multiphase homogenization models, which was originally presented in [7]. In the multiphase models, the media are not considered as several materials at each point of the space simultaneously.…”