Slope limiting for vectors: A novel vector limiting algorithm
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. Copyright (C) 2010 John Wiley & Sons, Ltd.
limiter algorithms lagrangian hydrodynamics ale-arbitrary lagrangian eulerian compressible flow euler equations finite volume methods shock capturing