Node-pair finite volume/finite element schemes for the Euler equation in cylindrical and spherical coordinates |
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Authors: | D De Santis G Geraci A Guardone |
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Institution: | 1. INRIA Bordeaux Sud-Ouest, Èquipe-projet Bacchus, Cours de la Libération, 33405 Talence, France;2. Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy |
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Abstract: | A numerical scheme is presented for the solution of the compressible Euler equations in both cylindrical and spherical coordinates. The unstructured grid solver is based on a mixed finite volume/finite element approach. Equivalence conditions linking the node-centered finite volume and the linear Lagrangian finite element scheme over unstructured grids are reported and used to devise a common framework for solving the discrete Euler equations in both the cylindrical and the spherical reference systems. Numerical simulations are presented for the explosion and implosion problems with spherical symmetry, which are solved in both the axial–radial cylindrical coordinates and the radial–azimuthal spherical coordinates. Numerical results are found to be in good agreement with one-dimensional simulations over a fine mesh. |
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Keywords: | Compressible flows Cylindrical coordinates Spherical coordinates Explosions Implosions Finite element/volume methods |
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