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Center for Nonlinear Studies |
The purpose of this talk is to present some of the works undertaken at CELIA laboratory (CEA, CNRS, Université Bordeaux I) in the field of numerical modeling of highly compressible fluid flows. This activity within the team Interaction-Inertial Confinement Fusion-Astrophysics, had as main objective the development of robust numerical schemes devoted to the numerical simulation of high energy density plasma physics. This work was realized by writing the CHIC code, which is a software for designing and restoring experience in the field of Inertial Confinement Fusion (ICF). The theoretical model describing the implosion of a laser target is a system of partial differential equations in the center of which is the Euler equations written in Lagrangian formalism, coupled with diffusion equations modeling the nonlinear transport of energy by electrons and photons. In this talk, after a brief review of the physical context, we describe two novel methods which constitute the backbone of the CHIC code. These are two high-order finite volume schemes respectively dedicated to solving the equations of Lagrangian hydrodynamics and the anisotropic diffusion equations on bi-dimensional unstructured grids. The first scheme, called EUCCLHYD (Explicit Unstructured Lagrangian Hydrodynamics), solves the equations of gas dynamics on a moving mesh that moves at the speed of the fluid. It is obtained from a general formalism based on the concept of sub-cell forces. In this context, the numerical fluxes are expressed in terms of the sub-cell force and the nodal velocity. Their determination is based on three basic principles: geometric compatibility between the movement of nodes and the volume change of mesh (Geometric Conservation Law), compatibility with the second law of thermodynamics and conservation of total energy and momentum. The high-order extension is performed using a method based on solving a generalized Riemann problem in the acoustic approximation. The second scheme, called CCLAD (Cell-Centered Lagrangian Diffusion), solves the anisotropic heat equation. The corresponding discretization relies on a discrete variational formulation based on the sub-cell that allows to build a multi-point approximation of heat flux. This high-order discretization makes possible the resolution of the equations of anisotropic diffusion with satisfactory accuracy on highly distorted Lagrangian meshes. The accuracy and robustness of these numerical methods are demonstrated on representative test cases.
Host: Mikhail Shashkov. shashkov@lanl.gov, 667-4400