SUMMARYWe present a new space-time SUPG formulation of the shallow-water equations. In this formulation, we use a stabilization parameter that was introduced for compressible flows and a new shock-capturing parameter. In the context of two test problems, we evaluate the performance of the new shock-capturing parameter. We also evaluate the performance of the space-time SUPG formulation compared to the semi-discrete SUPG formulation, where the system of semi-discrete equations is solved with the central-difference (Crank-Nicolson) time-integration algorithm.
SUMMARYThis paper describes an Eulerian formulation for large deformation solid dynamics. In the present Eulerian approach, an advective equation is solved using the Stream-Upwind/Petrov-Galerkin finite element method. The Eulerian finite element method is applied to path-dependent solid analyses such as impact bar and ductile necking problems. These computational results using the Eulerian finite element method are compared with the results obtained from using the Lagrangian finite element method and an Eulerian formulation based on a finite difference method.
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