THE HLLEM RIEMANN SOLVER FOR 3D MULTI-MATERIAL GAS DYNAMICS WITH AN ARBITRARY EQUATION OF STATE
I. V. Glazyrin, A. V. Ershova, N. A. Mikhailov
VANT. Ser.: Mat. Mod. Fiz. Proc 2023. Вып.4. С. 44-58.
The paper proposes the generalization of the HLLEM Riemann solver earlier used for a system of 1D single-material gas-dynamic equations onto a 3D multi-material case for an arbitrary unstructured mesh. Similarly to the 1D case, arbitrary equations of state (EOSes) of the materials are possible. The discontinuity is spread over a number of computational cells and in this domain the model of mixtures based on mass concentrations is used. The 3D multi-material gas-dynamic equation system is solved in Eulerian variables in Cartesian coordinate system. The equation system is simulated in its conservative form with the isothermal closure condition, i.e. equal temperatures of the materials are assumed. To implement the HLLEM solver, the right and left eigenvectors of the Jacobian matrix have been derived for the 3D multi-material gas-dynamic equation system with an arbitrary EOS. The proposed HLLEM solver has been implemented within the 3D Euler "Fokus" code using the finite volume method. The fluxes of conservative variables across faces of cells are calculated using the mean formula. The values of the fluxes of conservative quantities at the centers of cell faces can be found by considering 1D Riemann problems along normals to faces of cells. The reconstruction of the quantity values on the cell faces is performed using the TVD slope limiters. The time solution is found using the two-stage Runge-Kutta method. Two plane Riemann problems were selected for testing on a 3D cubic and an unstructured mesh with the ideal gas EOS and two-term EOS. The results of testing demonstrate the proposed approach efficiency. Keywords: multi-material gas dynamics, Riemann solver, HLLEM, eigenvectors, arbitrary equation of state, three-dimensional unstructured mesh.
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