Hybrid finite volume approach to Euler solutions for supersonic flows

Abstract

A new efficient numerical scheme is presented to solve the Euler equations about three-dimensional surfaces for supersonic flows. The approach utilizes a node-centered, physical space, finite-volume, central-difference scheme with added dissipation that is applied to the crossflow plane terms of the Euler equations. The discretized unsteady Euler equations are then solved by multistage Runge-Kutta integration with local time stepping and residual smoothing to accelerate convergence to a steady state. Three-dimensional flows are treated using an upwind finite-difference scheme for the nonconical terms within the context of a fully implicit marching technique on spherical surfaces. Results for both conical and three-dimensional flows are presented.