In this paper we report on recent developments concerning multidimensional upwind schemes for solving the Ruler equations on a grid composed of triangles. As a guideline we take the three concepts which constitute Roc’s one dimensional approximate Riemann solver: (1) an analytic eigenvector-or wave decomposition of the flux derivative; (2) a discrete counterpart using a conservative linearization of the flux difference over a cell; (3) an upwind distribution of the decomposed parts over the meshpoints according to the sign of the corresponding eigenvalues. Each of these three elements are generalized for multidimensional flow, avoiding a dimension by dimension analysis. Eigenvector decompositions for the two dimensional flux divergence (two-dimensional wave models) have been proposed in 1986. A discrete counterpart using a recently developed conservative linearization of the flux balance over a triangle is explained in more detail. Nonlinear positive and linearity preserving scalar upwind distribution schemes are described for the distribution of the decomposed parts. Numerical results on standard subsonic, transonic and supersonic test cases arc presented for different combinations of decom position and scalar distribution schemes on triangulated meshes. Although many of the theoretical and numerical alternatives are still open, these results indicate that the present approach is a viable generalization of the one dimensional Riemann solvers.

Progress on multidimensional upwind Euler solvers for unstructured grids / Struijs, R.; Deconinck, H.; De Palma, P.; Roe, P. L.; Powell, K. G.. - STAMPA. - 10th Computational Fluid Dynamics Conference:(1991). (Intervento presentato al convegno 10th AIAA Computational Fluid Dynamics Conference, AIAA Paper 91-1550 tenutosi a Honolulu, HI nel June 24-26,1991) [10.2514/6.1991-1550].

Progress on multidimensional upwind Euler solvers for unstructured grids

De Palma, P.;
1991-01-01

Abstract

In this paper we report on recent developments concerning multidimensional upwind schemes for solving the Ruler equations on a grid composed of triangles. As a guideline we take the three concepts which constitute Roc’s one dimensional approximate Riemann solver: (1) an analytic eigenvector-or wave decomposition of the flux derivative; (2) a discrete counterpart using a conservative linearization of the flux difference over a cell; (3) an upwind distribution of the decomposed parts over the meshpoints according to the sign of the corresponding eigenvalues. Each of these three elements are generalized for multidimensional flow, avoiding a dimension by dimension analysis. Eigenvector decompositions for the two dimensional flux divergence (two-dimensional wave models) have been proposed in 1986. A discrete counterpart using a recently developed conservative linearization of the flux balance over a triangle is explained in more detail. Nonlinear positive and linearity preserving scalar upwind distribution schemes are described for the distribution of the decomposed parts. Numerical results on standard subsonic, transonic and supersonic test cases arc presented for different combinations of decom position and scalar distribution schemes on triangulated meshes. Although many of the theoretical and numerical alternatives are still open, these results indicate that the present approach is a viable generalization of the one dimensional Riemann solvers.
1991
10th AIAA Computational Fluid Dynamics Conference, AIAA Paper 91-1550
Progress on multidimensional upwind Euler solvers for unstructured grids / Struijs, R.; Deconinck, H.; De Palma, P.; Roe, P. L.; Powell, K. G.. - STAMPA. - 10th Computational Fluid Dynamics Conference:(1991). (Intervento presentato al convegno 10th AIAA Computational Fluid Dynamics Conference, AIAA Paper 91-1550 tenutosi a Honolulu, HI nel June 24-26,1991) [10.2514/6.1991-1550].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/17062
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