Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

Abstract

A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation tenns, and by refonnulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about arbitrary configurations.

Order of accuracy study of unstructured grid finite volume upwind schemes

“…2, the coordinates of the vertices, which define the interface between cells i and k. These points are always ordered in the counterclockwise direction for each i-th control volume. Note that, in the case of the Euler equations, artificial dissipation terms must be added in order to control nonlinear instabilities (Mavriplis, 1990). In the present linear scalar case, artificial dissipation terms are not required and they were not used in the simulations here reported.…”

A study of convective flux schemes for aerospace flows

“…The A i matrix coefficient in Eq. (6) is replaced by a scalar coefficient (Mavriplis, 1988;Mavriplis, 1990) defined as…”

“…In the centered case, explicit addition of artificial dissipation terms is required to control nonlinear instabilities in the numerical solution. For computation of these terms in the current work, both the scalar and the matrix versions of a switched secondand fourth-difference scheme are considered (Mavriplis, 1990;Turkel and Vatsa, 1994). The Convective-Upwind Split-Pressure (CUSP) artificial dissipation model (Jameson, 1995a;Jameson, 1995b) is also considered in the centered scheme case.…”

A Direct Adaptive Poisson Solver of Arbitrary Order Accuracy

“…Good coarsening strategies can be found in [1,27] for locally uniform meshes based on adaptive mesh refinement [5,6]. Other useful schemes have been designed for composite overlapping grids [4,13], quad-trees [14,25], and unstructured triangulations [3,12,21].…”