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Center for Nonlinear Studies |
We present a new Lagrangian cell-centered scheme for two—dimensional compressible flows. The primary variables in this new scheme are cell-centered, that is, density, momentum and total energy are defined by their mean values in the cells. The vertex velocities and the numerical fluxes through the cell interfaces are not computed independently as usual but in a consistent manner thanks to an original solver located at the nodes. The main new features of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. Thanks to this extra degrees of freedom we are able to construct this solver at vertices so that it fulfills two properties. First, the conservation of momentum and total energy is ensured. Second, a semi--discrete entropy inequality is provided. In the case of a one dimensional flow, the solver reduces to the classical Godunov acoustic solver: it can be considered as its two--dimensional generalization. Many numerical tests are presented. They are representative test cases for compressible flows and demonstrate the robustness and the accuracy of this new solver.
Host: Mikhail Shashkov