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This paper is focused on the Residual Distribution (RD) interpretation of the Do-4 brev et al. scheme [Dobrev et al., SISC, 2012] for the numerical solution of the Euler equations 5 in Lagrangian form. The first ingredient of the original scheme is the staggered grid formulation 6 which uses continuous node-based finite element approximations for the kinematic variables and cell-7 centered discontinuous finite elements for the thermodynamic parameters. The second ingredient of 8 the Dobrev et al. scheme is an artificial viscosity technique applied in order to make possible the 9 computation of strong discontinuities. The aim of this paper is to provide an efficient mass matrix 10 diagonalization method in order to avoid the inversion of the global sparse mass matrix while keep-11 ing all the accuracy properties and to construct a parameter-free stabilization of the scheme to get 12 rid of the artificial viscosity. In addition, we study the conservation and entropy properties of the 13 constructed RD scheme. To demonstrate the robustness of the proposed RD scheme, we solve several 14 one-dimensional shock tube problems from rather mild to very strong ones. This paper also illus-15 trates a general technique that enables, from a non conservative formulation of a system that has a 16 conservative formulation, how to design a numerical approximation that will provably give sequences 17 of solution converging to a weak solution of the problem. This enable to use directly variables that 18 are more pertinent, from an engineering point of view, than the standard conserved variables: here 19 the specific internal energy. 20
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Dates and versions

hal-01327473 , version 1 (06-06-2016)
hal-01327473 , version 2 (02-05-2017)


  • HAL Id : hal-01327473 , version 2


Remi Abgrall, Tokareva Svetlana. STAGGERED GRID RESIDUAL DISTRIBUTION SCHEME: Staggered grid RD scheme for Lagrangian hydrodynamics. 2016. ⟨hal-01327473v2⟩


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