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Center for Nonlinear Studies |
In this talk, we present a general framework for high-order Lagrangian discretization of the compressible shock hydrodynamics equations using curvilinear finite elements in 2D, 3D and axisymmetric geometries. Our method is derived through a variational formulation of the momentum and energy conservation equations using high-order continuous finiteq elements for the velocity and position, and high-order discontinuous basis for the internal energy field. In particular, high-order position values enable curvilinear zone geometries allowing for better approximation of the mesh curvature which develops naturally with the flow. The semi-discrete equations involve velocity and energy 'mass matrices' which are constant in time due to our notion of strong mass conservation. We also introduce the concept of generalized corner force matrices, which together with the strong mass conservation principle, imply the exact total energy conservation on a semidiscrete level. The fully-discrete equations are obtained by the application of Runge Kutta-like energy conserving time stepping scheme. We present a number of 2D, 3D and axisymmetric computational results demonstrating the benefits of the high-order approach for Lagrangian computations, including improved robustness and symmetry preservation, significant reduction in mesh imprinting, and high-order convergence for smooth problems.
Host: Mikhail Shashkov. shashkov@lanl.gov, 667-4400