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Slope limiting for vectors: A novel vector limiting algorithm. (English) Zbl 1453.76100
Summary: Slope or flux limiters are used in high-order methods to maintain monotonicity of the solution near discontinuities. For vectors or tensors, these limiters are applied separately to each component. Such a procedure is inherently frame-dependent and can break rotational or planar symmetries present in a problem. Instead, we propose a new frame-invariant VIP monotonicity criterion for vectors. We use this new concept to formulate a VIP slope-limiter for the SMG/Q scheme for Lagrangian hydrodynamics. The new limiter is found to improve symmetry preservation in a number of test problems, including the Saltzman test, 2D and 3D Sedov-Taylor problems, and 2D Noh problem.

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
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