An annurate finite volume scheme for euler and navier-stokes equations on unstructured adaptive grids

摘要

This paper presents a finite volume cell-centered technique for computing steady state solutions of the full Euler and Navier-Stokes equations on unstructured meshes. We aim to design a scheme which is the most possible insensitive to grid distortions, while however remaining of practical interest in terms of CPU time, storage and convergence. For that purpose, we use an original quadratic reconstruction with a fixed stencil and a high order flux integration by the Gauss quadrature rule to compute the advective term of the equations. Time evolution is presently performed with an explicit multi-step Runge-Kutta scheme. A very general adaptation procedure based on h-refinement and coarsening is employed to improve the resolution of complex flow features. The accuracy of the method is demonstrated for a liner equation and for inviscid and viscous flow computations. The inviscid flow over the NACA0012 airfoil is computed at various Mach numbers. These calculations illustrate the effectiveness of the adaptation procedure. We investigate the supersonic flow over a compression ramp to validate the Navier-Stokes solver by using a hybrid grid.