Arbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume method

In this article, we propose a novel high-order multi-moment finite volume method (MMFVM) for solving linear and nonlinear hyperbolic systems on unstructured grids. Different from the previous versions of volume-average/point-value multi-moment (VPM) scheme, the present scheme is developed by using a new reconstruction procedure based on the constrained least-square method which can be naturally extended to arbitrary highorder of accuracy in two and three dimensions. The so-called VPM-CLS (VPM based on constrained least-square method) scheme substantially increases the solution accuracy on a compact stencil which largely simplifies the computations. In order to eliminate the numerical oscillations associated with high-order schemes, we propose a new limiting projection approach named AOD (adaptive order detection) to choose the optimal degree of reconstruction polynomial for trouble cells in presence of discontinuous solutions. The resulting reconstruction method, i.e. VPM-AOD that combines VPM-CLS scheme with AOD limiting projection technique is able to attain 5th-order accuracy on the stencil of all immediately adjacent cells and achieve essentially non-oscillatory and less-dissipative numerical results for discontinuous solutions. The numerical methods are extensively verified by various benchmark tests for the Euler equations of compressible gas dynamics. Numerical results demonstrate the high solution accuracy and excellent capabilities of proposed schemes to handle both complex physics and geometries. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

In this article, a novel high-order multi-moment finite volume method (MMFVM) for solving linear and nonlinear hyperbolic systems on unstructured grids is proposed. The method, combining VPM-CLS scheme with AOD limiting projection technique, achieves high accuracy and non-oscillatory numerical results for discontinuous solutions.