Accuracy assessment of a high-order moving least squares finite volume method for compressible flows

This paper proposes an investigation of some important properties of a high-order finite-volume moving least-squares based method (FV-MLSs) for the solution of two-dimensional Euler and Navier–Stokes equations on unstructured grids. A particular attention is paid to the computation of derivatives of shape functions by means of diffuse or full discretization. Furthermore, we introduce the semi-diffuse approach, which is a compromise in terms of accuracy and computational cost. In addition, we investigate the influence of the curvature of wall boundary conditions on the proposed numerical scheme. As expected, we found an improvement when the walls’ curvature is taken into account. However, and differently as in discontinuous Galerkin schemes, the use of a straight representation of the wall normals does not induce a substantial loss of accuracy. Numerical simulations show the accuracy and the robustness of the numerical approach for both inviscid and viscous flows.

► Some important properties of a finite-volume moving least-squares method are studied.
► A particular attention is paid to the computation of shape function derivatives.
► High-order schemes for compressible flows on unstructured grid are then developed.
► Straight representation of wall normals does not induce important looses of accuracy.
► Accuracy and robustness are assessed for both inviscid and viscous flows.