An edge-based unstructured mesh formulation for high speed tridimensional compressible flow simulation

Abstract

Numerical simulation of realistic compressible flows is very important and requires accurate and flexible tridimensional formulations, which should furthermore be robust and efficient. In this work we describe the development of a computational tool for numerical simulation of inviscid compressible 3-D fluid flow problems. This tool uses as the main building block an edge-based Galerkin FEM (Finite Element Method) together with a MUSCL (Monotonic Upstream-centered Schemes for Conservations Laws) approach to get a higher-order scheme with LED (Local Extremum Diminishing) property. The code is particularly developed for the simulation of supersonic and hypersonic flow regimes and several important (sometimes unavoidable) numerical procedures incorporated to increase its robustness are described. Some aspects related to the adoption of an edge-based data structure and other implementation issues are also described. Finally, some numerical model problems are analyzed and compared with results found in the literature demonstrating the effectiveness of the developed tool