EBR schemes with curvilinear reconstructions for hybrid meshes

Abstract

In this paper, the vertex-centered EBR schemes, originally developed for solving the Euler and Navier–Stokes equations on unstructured tetrahedral meshes, are generalized to unstructured mixed-element meshes. In these schemes, the convective flux is approximated using quasi-1D edge-oriented reconstructions. On hybrid mixed-element meshes with layers of highly anisotropic prismatic cells that are commonly used in simulations of external turbulent flows, the quasi-1D reconstructions may lead to significantly irregular stencils, which cause both larger approximation error and computational instability. To improve accuracy and robustness of the EBR schemes on these meshes, we propose to use curvilinear reconstructions of variables. We present algorithms of constructing curvilinear stencils and validate the resulting schemes on a series of 2D and 3D problems such as an acoustic wave within an infinite cylinder in the presence of viscosity and thermal conduction, turbulent flows around the NACA0012 airfoil and the Caradonna-Tung helicopter rotor. In all these cases, the curvilinear reconstructions improve accuracy of the numerical solutions with no extra computational cost.