A 3-D least-squares upwind Euler solver for unstructured meshes

Abstract

A three-dimensional finite-volume upwind Euler solver is developed for unstructured meshes. The finite-volume scheme solves for solution variables at vertices of the mesh and satisfies the integral conservation law on nonoverlapping polyhedral control volumes surrounding vertices of the mesh. The schene achieves improved solution accuracy by assuming a piecewise linear variation of the solution in each control volume. This improved spatial accuracy hinges heavily upon the calculation of the solution gradient in each control volume given pointwise values of the solution at vertices of the mesh. Several algorithms are discussed for obtaining these gradients. Details concerning implementation procedures and data structures are discussed. Sample calculations for inviscid Euler flow about isolated aircraft wings at subsonic and transonic speeds are compared with established Euler solvers as well as experiment.