A hybrid pressure-density-based Mach uniform algorithm for 2D Euler equations on unstructured grids by using multi-moment finite volume method

作者：Xie Bin^*; Deng Xi; Sun Ziyao; Xiao Feng^*

来源：Journal of Computational Physics, 2017, 335: 637-663.

DOI：10.1016/j.jcp.2017.01.043

• Euler equations
• Unstructured grid
• Mach uniform solver
• Finite volume method
• Pressure-correction projection
• Multi-moment reconstruction
• Numerical oscillation
• Numerical dissipation

We propose a novel Mach-uniform numerical model for 2D Euler equations on unstructured grids by using multi-moment finite volume method. The model integrates two key components newly developed to solve compressible flows on unstructured grids with improved accuracy and robustness. A new variant of AUSM scheme, so-called AUSM(+) -pcp (AUSM(+) with pressure-correction projection), has been devised including a pressure correction projection to the AUSM(+) flux splitting, which maintains the exact numerical conservativeness and works well for all Mach numbers. A novel 3th-order, non-oscillatory and less-dissipative reconstruction has been proposed by introducing a multi-dimensional limiting and a BVD (boundary variation diminishing) treatment to the VPM (volume integrated average (VIA) and point value (PV) based multi-moment) reconstruction. The resulting reconstruction scheme, the limited VPM-BVD formulation, is able to resolve both smooth and non-smooth solutions with high fidelity. Benchmark tests have been used to verify the present model. The numerical results substantiate the present model as an accurate and robust unstructured-grid formulation for flows of all Mach numbers.

• 出版日期2017-4-15