A kinetic scheme with variable velocities and relative entropy
Abstract
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average velocities, one in each quadrant. In the associated finite volume scheme, the average velocities are used to enforce the Rankine-Hugoniot jump conditions for the numerical diffusion at cell-interfaces, thereby capturing steady discontinuities exactly. The variable range of velocities is used to provide additional diffusion in smooth regions. Further, a novel kinetic theory based expression for relative entropy is presented which, along with an additional criterion, is used to identify expansions and smooth flow regions. Appropriate flow tangency and far-field boundary conditions are formulated for the proposed kinetic model. Several benchmark 1D and 2D compressible flow test cases are solved to demonstrate the efficacy of the proposed solver.
Cite
@article{arxiv.2304.02520,
title = {A kinetic scheme with variable velocities and relative entropy},
author = {Shashi Shekhar Roy and S. V. Raghurama Rao},
journal= {arXiv preprint arXiv:2304.02520},
year = {2023}
}