×

zbMATH — the first resource for mathematics

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.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] van Leer, Towards the ultimate conservative difference scheme V, Journal of Computational Physics 32 pp 101– (1979) · Zbl 1364.65223
[2] Ben-Artzi, The Generalized Riemann Problem in Computational Fluid dynamics (2003) · Zbl 1017.76001
[3] van Leer, Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme, Journal of Computational Physics 14 pp 361– (1974) · Zbl 0276.65055
[4] Loubère R On the effect of the different limiters for the tensor artificial viscosity for the Compatible Lagrangian Hydrodynamics Scheme 2005
[5] Zalesak, Fully multidimensional flux corrected transport algorithms for fluids, Journal of Computational Physics 31 pp 335– (1979) · Zbl 0416.76002
[6] Dukowicz, Accurate conservative remapping (rezoning) for Arbitrary Lagrangian-Eulerian computations, SIAM Journal on Scientific and Statistical Computing 8 pp 305– (1987) · Zbl 0644.76085
[7] Barth TJ Jesperson DC The design and application of upwind schemes on unstructured meshes
[8] Jameson, Computational algorithms for aerodynamic analysis and design, Applied Numerical Mathematics 13 (5) pp 383– (1993) · Zbl 0792.76049
[9] Rider WJ Kothe DB Constrained minimization for monotonic reconstruction 1997
[10] Hubbard, Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids, Journal of Computational Physics 155 pp 54– (1999) · Zbl 0934.65109
[11] Berger M Aftosmis MJ Murman SM Analysis of slope limiters on Irregular Grids 2005
[12] Boris, Flux corrected transport, SHASTA, a fluid transport algorithm that works, Journal of Computational Physics 11 pp 38– (1973) · Zbl 0251.76004
[13] Harten, High resolution schemes for hyperbolic conservation laws, Journal of Computational Physics 49 pp 357– (1983) · Zbl 0565.65050
[14] Sweby, High-resolution schemes using flux limiters for hyperbolic conservation laws, SIAM Journal on Numerical Analysis 21 pp 995– (1984) · Zbl 0565.65048
[15] Luttwak, Shock Compression of Condensed Matter-2001 pp 255– (2002)
[16] Luttwak G Falcovitz J 2005 www.extra.rdg.ac.uk/ifcd/Multimaterial-Workshop.htm
[17] Luttwak, Shock Compression of Condensed Matter-2005 pp 339– (2006)
[18] Luttwak G 2007 www-troja.fjfi.cvut.cz/multimat07
[19] Luttwak G Falcovitz J Applying the SMG scheme to reactive flows
[20] Saltzman J Colella P Second order upwind transport methods for Lagrangian hydrodynamics 1985
[21] O’Rourke, Computational Geometry in C (1998) · Zbl 0912.68201
[22] Christensen RB Godunov methods on a staggered mesh. An improved artificial viscosity 1990
[23] Caramana, Formulation of artificial viscosity for multi-dimensional shock computations, Journal of Computational Physics 144 pp 70– (1998) · Zbl 1392.76041
[24] Vitello P Souers PC Stability effects of artificial viscosity in detonation modeling
[25] Noh, Errors for calculations of strong shocks with artificial viscosity, Journal of Computational Physics 72 pp 78– (1987) · Zbl 0619.76091
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.