2024/03/21 by Shashi Shekhar Roy, Roy, Shashi Shekhar, S. V. Raghurama Rao +1
Engineering · Materials Science · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #High-Velocity Impact and Material Behavior
paper · pdf · doi:10.48550/arxiv.2403.14794
openalex publication_date 2024/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
In this paper, we present a kinetic model with flexible velocities that satisfy positivity preservation conditions for the Euler equations. Our 1D kinetic model consists of two velocities and employs both the asymmetrical and symmetrical models. Switching between the two models is governed by our formulation of kinetic relative entropy along with an additional criterion to ensure an accurate, entropic, and robust scheme. In 2D, we introduce a novel three-velocity kinetic model, defined to ensure a locally one-dimensional formulation for the resulting macroscopic normal flux. For first order accuracy, we also obtain a limit on the time step which ensures positivity preservation. The resulting numerical scheme captures grid-aligned steady shocks exactly. Several benchmark compressible flow test cases are solved in 1D and 2D to demonstrate the efficacy of the proposed solver.