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 © 2010 John Wiley & Sons, Ltd.

[1]  P. Sweby.  High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , 1984 .

[2]  Mikhail Shashkov,et al.  Formulations of Artificial Viscosity for Multi-dimensional Shock Wave Computations , 1998 .

[3]  William J. Rider,et al.  Constrained minimization for monotonic reconstruction , 1997 .

[4]  John K. Dukowicz,et al.  Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations , 1987 .

[5]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[6]  M. Berger,et al.  Analysis of Slope Limiters on Irregular Grids , 2005 .

[7]  Timothy J. Barth,et al.  The design and application of upwind schemes on unstructured meshes , 1989 .

[8]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[9]  Jay P. Boris,et al.  Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works , 1973 .

[10]  Matthew E. Hubbard,et al.  Regular Article: Multidimensional Slope Limiters for MUSCL-Type Finite Volume Schemes on Unstructured Grids , 1999 .

[11]  A. Harten.  High Resolution Schemes for Hyperbolic Conservation Laws , 2017 .

[12]  W. F. Noh.  Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux , 1985 .

[13]  S. Zalesak.  Fully multidimensional flux-corrected transport algorithms for fluids , 1979 .

[14]  A. Jameson.  Computational algorithms for aerodynamic analysis and design , 1993 .

[15]  Applying the SMG Scheme to Reactive Flow , 2010 .