A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations

• Published in: Journal of computational physics 2021-01, Vol.425, p.109906, Article 109906
• Main Authors: Li, Maojun, Cheng, Yongping, Shen, Jie, Zhang, Xiangxiong
• Format: Article
• Language: English
• Subjects: Bound-preserving scheme; Computational fluid dynamics; Computational physics; Density; Discontinuous Galerkin method; Evolution; Finite element method; Finite volume method; Fluid flow; Galerkin method; Mathematical analysis; Momentum; Naiver-Stokes equations; Navier-Stokes equations; Numerical methods; Runge-Kutta method; Variable density incompressible flows
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2020.109906

•This is a high order accurate and strictly bound-preserving scheme for variable density incompressible flows.•A high order DG method is used for density and continuous finite element method is used for velocity.•A variable coefficient pressure Poisson equation is solved to recover pressure.•A third order IMEX SSP Runge-Kutta method is used for both bound-preserving and avoiding small time steps. For numerical schemes to the incompressible Navier-Stokes equations with variable density, it is a critical property to preserve the bounds of density. A bound-preserving high order accurate scheme can be constructed by using high order discontinuous Galerkin (DG) methods or finite volume methods with a bound-preserving limiter for the density evolution equation, with any popular numerical method for the momentum evolution. In this paper, we consider a combination of a continuous finite element method for momentum evolution and a bound-preserving DG method for density evolution. Fully explicit and explicit-implicit strong stability preserving Runge-Kutta methods can be used for the time discretization for the sake of bound-preserving. Numerical tests on representative examples are shown to demonstrate the performance of the proposed scheme.