A Compatible Lagrangian Hydrodynamics Algorithm for Unstructured Grids

James C. Campbell, Mikhail J. Shashkov

Abstract


We have extended a compatible Lagrangian hydrodynamics algorithm to unstructured grids, where each zone is a polygon with an arbitrary number of sides. An unstructured grid offers more flexibility than a logical grid in the construction of the initial grid, especially for domains with complex geometry. The compatible hydrodynamics algorithm is designed to conserve momentum and total energy exactly in discrete form. It achieves this by deriving the discrete energy equation from the discrete momentum equation using the conservation of total energy. The compatible hydrodynamics algorithm includes subzonal pressures, which are used to control spurious grid motions, and an edge-centered artificial viscosity. The edge-centered viscosity uses a limiter function to ensure that the viscosity switches off under uniform compression and rotation. On a logical grid this limiter function uses the local coordinate system to determine neighbor edges. On an unstructured grid a local coordinate system at a node can not be used, requiring instead alternative methods for selecting neighbor edges. Computational results show that the algorithm functions well on an unstructured grid.

Keywords


Lagrangian hydrodynamics algorithm; unstructured grid.

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