Abstract
Recently ((1, 2)) we have formulated a new frame invariant monotonicity cri- terion and slope limiter for vectors and applied it to the Lagrangian phase of the SMG/Q scheme. This Vector Image Polygon/Polyhedron (VIP) limiter was shown to improve sym- metry preservation in a set of test problems. In this study we implement the VIP limiter also to the momentum advection phase of the SMQ/Q scheme for (Arbitrary Lagrangian Eulerian) ALE hydrodynamics. The 2D cylindrical Noh problem serves as a test case to demonstrate the effect of the VIP limiter on symmetry preservation.
Highlights
Second order Godunov ([3, 4]) and several other high resolution schemes use the gradients of the variables to compute the flux terms required in the solution of the conservation laws
Its formulation is based on a convex hull of a Vector Image Polygon/Polyhedron (VIP) (Vector Image Polygon or Polyhedron), and it was applied to the Lagrangian phase of the SMG scheme
The 2D cylindrical Noh problem was run in ALE mode, serving to assess the performance of the VIP limiter in ALE calculations
Summary
Second order Godunov ([3, 4]) and several other high resolution schemes use the gradients of the variables to compute the flux terms required in the solution of the conservation laws. In hyperbolic partial differential equations discontinuities may be present or can evolve in time At these (captured) discontinuities the gradients are not well defined and using them directly can produce unphysical fluctuations in the solution. Such schemes must use flux or slope limiters to prevent monotonicity violations. For vectors or tensors the limiters are usually applied separately to each component. Such a procedure is inherently frame dependent and does not preserve the rotational or planar symmetries present in a problem. Its formulation is based on a convex hull of a VIP (Vector Image Polygon or Polyhedron), and it was applied to the Lagrangian phase of the SMG scheme. The 2D cylindrical Noh problem was run in ALE mode, serving to assess the performance of the VIP limiter in ALE calculations
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