Solutions of The Euler and The Navier-Stokes Equations Using The Jameson and Mavriplis and The Liou Steffen Unstructured Algorithms in Three-Dimensions

Abstract

In the present work, the Jameson and Mavriplis and the Liou and Steffen unstructured algorithms are applied to solve the Euler and the Navier-Stokes equations in three-dimensions. The governing equations in conservative form are solved, employing a finite volume formulation and an unstructured spatial discretization. The Jameson and Mavriplis algorithm is a symmetrical second-order one, while the Liou and Steffen algorithm is a flux vector splitting first-order upwind one. Both schemes use a second-order Runge-Kutta method to perform time integration. The steady state problems of the supersonic flow along a ramp and of the "cold gas" hypersonic flow along a diffuser are studied. The results have demonstrated that both schemes predict appropriately the shock angles at the ramp and at the lower and upper walls of the diffuser, in the inviscid case. In the viscous study, only the Liou and Steffen scheme yielded converged results, obtaining good ramp shock angles.