A novel multiscale discrete velocity method for model kinetic equations

• Published in: Communications in nonlinear science & numerical simulation 2021-01, Vol.92, p.105473, Article 105473
• Main Authors: Yuan, Ruifeng, Liu, Sha, Zhong, Chengwen
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Continuum flow; Discrete velocity method; Distribution functions; Gas flow; Kinetic equations; Kinetic scheme; Kinetics; Low speed; Multiscale scheme; Navier-Stokes equations; Numerical dissipation; Rarefied gas flow; Variables
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2020.105473

•A new and concise strategy to achieve multiscale property for the scheme based on discrete velocity framework is presented.•The excess numerical dissipation of the conventional DVM in the continuum flow regime is shown and the cause is revealed.•A multiscale DVM is pr esented with concise form and good performance in all flow regimes. This paper focuses on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methodsrepresented by unified gas-kinetic scheme (UGKS) and discrete unified gas-kinetic scheme (DUGKS), which concentrate on the evolution of the distribution function at the cell interface, in the present scheme the flux for macroscopic variables is split into the equilibrium part and the nonequilibrium part, and the nonequilibrium flux is calculated by integrating the discrete distribution function at the cell center, which overcomes the excess numerical dissipation of the conventional DVM in the continuum flow regime. Afterwards, the macroscopic variables are finally updated by simply integrating the discrete distribution function at the cell center, or by a blend of the increments based on the macroscopic and the microscopic systems, and the multiscale property is achieved. Several test cases, involving unsteady, steady, high speed, low speed gas flows in all flow regimes, have been performed, demonstrating the good performance of the multiscale DVM from free molecule to continuum Navier-Stokes solutions and the multiscale property of the scheme is proved.