Curvilinear Reconstructions for EBR Schemes On Semi-Structured Meshes

Abstract

The vertex-centered edge-based reconstruction (EBR) schemes for solving Eulertype equations are originally developed for tetrahedral unstructured meshes and imply the usage of quasi-one-dimensional straight-line reconstructions to calculate the flux. However, on the hybrid unstructured meshes with layers of highly anisotropic prismatic cells that are commonly used in simulations of turbulent flows with boundary layers, the straight-line reconstructions may lead to strongly irregular stencils, which cause both larger approximation errors and computational instabilities. To improve the accuracy and stability characteristics of EBR schemes on such meshes, we propose to use the curvilinear reconstructions for the flux computation. In this paper, we describe the principles and algorithms of constructing curvilinear reconstructions on the structured and semi-structured prismatic meshes. The modified EBR schemes are tested on the well-known NACA 0012 airfoil validation case for both two-dimensional and three-dimensional formulations, and the obtained numerical results are discussed in detail.