Toward accurate and efficient multi-moment finite volume method for large eddy simulations of compressible flows on unstructured grids

Abstract

A novel multi-moment finite volume method is proposed for the solutions of linear and nonlinear hyperbolic equations on unstructured grids and further investigated for implicit large eddy simulation of compressible turbulence. Different from the previous volume integrated average and point value based multi-moment (VPM) method, the present scheme first reconstructs the solution values and first-order derivatives at boundary surfaces and then constructs a quadratic polynomial over each cell using Gauss divergence theorem. It eliminates the need to directly compute second derivatives of solution variables, which is more efficient than conventional finite volume discretizations at third-order accuracy. The so-called VPM-FR (VPM with face-based reconstruction) formulates novel spatial reconstruction within a compact stencil consisting of only face neighbouring cells, which substantially improves the numerical accuracy, efficiency, robustness as well as algorithmic simplicity. Fourier analysis is also conducted to verify the numerical properties of VPM-FR which are compared against the previous version of VPM scheme. Besides, a new limiting projection approach is devised to use a high-order limiter function which effectively suppresses the numerical oscillation in the vicinity of discontinuities. Numerical results of various benchmark tests are presented for the advection, Euler and Navier-Stokes equations which validate the excellent performance of VPM-FR scheme that well resolves broadband turbulence and the sharp shock profiles with a reduction in computation cost.