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- Q6719085 subject Q7138878.
- Q6719085 subject Q8407473.
- Q6719085 subject Q8690272.
- Q6719085 abstract "In the study of partial differential equations, the MUSCL scheme is a finite volume method that can provide highly accurate numerical solutions for a given system, even in cases where the solutions exhibit shocks, discontinuities, or large gradients. MUSCL stands for Monotonic Upstream-Centered Scheme for Conservation Laws (van Leer, 1979), and the term was introduced in a seminal paper by Bram van Leer (van Leer, 1979). In this paper he constructed the first high-order, total variation diminishing (TVD) scheme where he obtained second order spatial accuracy.The idea is to replace the piecewise constant approximation of Godunov's scheme by reconstructed states, derived from cell-averaged states obtained from the previous time-step. For each cell, slope limited, reconstructed left and right states are obtained and used to calculate fluxes at the cell boundaries (edges). These fluxes can, in turn, be used as input to a Riemann solver, following which the solutions are averaged and used to advance the solution in time. Alternatively, the fluxes can be used in Riemann-solver-free schemes, such as the Kurganov and Tadmor scheme outlined below.".
- Q6719085 thumbnail StepFirstOrdUpwind.png?width=300.
- Q6719085 wikiPageExternalLink Amir_Kabir.pdf.
- Q6719085 wikiPageExternalLink KT_semi-discrete.JCP00-centpack.pdf.
- Q6719085 wikiPageExternalLink Kur-Lev_3rd_semi_discrete.SINUM00-centpack.pdf.
- Q6719085 wikiPageExternalLink NT2.JCP90-centpack.pdf.
- Q6719085 wikiPageExternalLink gees.
- Q6719085 wikiPageWikiLink Q1023483.
- Q6719085 wikiPageWikiLink Q10741267.
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- Q6719085 wikiPageWikiLink Q214967.
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- Q6719085 wikiPageWikiLink Q249748.
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- Q6719085 wikiPageWikiLink Q324083.
- Q6719085 wikiPageWikiLink Q375175.
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- Q6719085 wikiPageWikiLink Q44528.
- Q6719085 wikiPageWikiLink Q4654996.
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- Q6719085 wikiPageWikiLink Q5463027.
- Q6719085 wikiPageWikiLink Q6153788.
- Q6719085 wikiPageWikiLink Q6485344.
- Q6719085 wikiPageWikiLink Q7138878.
- Q6719085 wikiPageWikiLink Q725944.
- Q6719085 wikiPageWikiLink Q7553155.
- Q6719085 wikiPageWikiLink Q7828154.
- Q6719085 wikiPageWikiLink Q83303.
- Q6719085 wikiPageWikiLink Q8407473.
- Q6719085 wikiPageWikiLink Q8690272.
- Q6719085 comment "In the study of partial differential equations, the MUSCL scheme is a finite volume method that can provide highly accurate numerical solutions for a given system, even in cases where the solutions exhibit shocks, discontinuities, or large gradients. MUSCL stands for Monotonic Upstream-Centered Scheme for Conservation Laws (van Leer, 1979), and the term was introduced in a seminal paper by Bram van Leer (van Leer, 1979).".
- Q6719085 label "MUSCL scheme".
- Q6719085 depiction StepFirstOrdUpwind.png.