Abstract

A numerical approach to solve a new coupled stochastic kinetic–fluid model is proposed in this paper. The approach yields a stable numerical scheme in the hydrodynamic limit as the Knudsen number goes to zero along the transition from kinetic regime to macroscopic regime. The method is based on the Odd-Even decomposition of the kinetic stochastic chemotaxis–fluid model which leads to an implicit-explicit scheme based on a two steps splitting strategy. The method is numerically validated by various tests in two dimensional space.

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