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- MUSCL_scheme 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.".
- MUSCL_scheme thumbnail StepFirstOrdUpwind.png?width=300.
- MUSCL_scheme wikiPageExternalLink Amir_Kabir.pdf.
- MUSCL_scheme wikiPageExternalLink index.php?nav=gees.
- MUSCL_scheme wikiPageExternalLink KT_semi-discrete.JCP00-centpack.pdf.
- MUSCL_scheme wikiPageExternalLink Kur-Lev_3rd_semi_discrete.SINUM00-centpack.pdf.
- MUSCL_scheme wikiPageExternalLink NT2.JCP90-centpack.pdf.
- MUSCL_scheme wikiPageID "5732212".
- MUSCL_scheme wikiPageLength "26037".
- MUSCL_scheme wikiPageOutDegree "49".
- MUSCL_scheme wikiPageRevisionID "658672232".
- MUSCL_scheme wikiPageWikiLink AUSM.
- MUSCL_scheme wikiPageWikiLink Bram_van_Leer.
- MUSCL_scheme wikiPageWikiLink Category:Computational_fluid_dynamics.
- MUSCL_scheme wikiPageWikiLink Category:Fluid_dynamics.
- MUSCL_scheme wikiPageWikiLink Category:Numerical_differential_equations.
- MUSCL_scheme wikiPageWikiLink Communications_on_Pure_and_Applied_Mathematics.
- MUSCL_scheme wikiPageWikiLink Courant–Friedrichs–Lewy_condition.
- MUSCL_scheme wikiPageWikiLink Eitan_Tadmor.
- MUSCL_scheme wikiPageWikiLink Equation_of_state.
- MUSCL_scheme wikiPageWikiLink Euclidean_vector.
- MUSCL_scheme wikiPageWikiLink Euler_equations_(fluid_dynamics).
- MUSCL_scheme wikiPageWikiLink File:LinExtrap.jpg.
- MUSCL_scheme wikiPageWikiLink File:ParabolicExtrap.jpg.
- MUSCL_scheme wikiPageWikiLink File:SodProbKTospre.png.
- MUSCL_scheme wikiPageWikiLink File:SodProbParabolicKTalbada.png.
- MUSCL_scheme wikiPageWikiLink File:StepFirstOrdUpwind.png.
- MUSCL_scheme wikiPageWikiLink File:StepKTsuperbee.png.
- MUSCL_scheme wikiPageWikiLink File:StepParabolicKTalbada.png.
- MUSCL_scheme wikiPageWikiLink File:StepSecOrdCentralDifference.png.
- MUSCL_scheme wikiPageWikiLink Finite_difference.
- MUSCL_scheme wikiPageWikiLink Finite_volume_method.
- MUSCL_scheme wikiPageWikiLink Flux.
- MUSCL_scheme wikiPageWikiLink Flux_limiter.
- MUSCL_scheme wikiPageWikiLink Fortran.
- MUSCL_scheme wikiPageWikiLink Godunovs_scheme.
- MUSCL_scheme wikiPageWikiLink Godunovs_theorem.
- MUSCL_scheme wikiPageWikiLink High-resolution_scheme.
- MUSCL_scheme wikiPageWikiLink High_resolution_scheme.
- MUSCL_scheme wikiPageWikiLink International_System_of_Units.
- MUSCL_scheme wikiPageWikiLink Method_of_lines.
- MUSCL_scheme wikiPageWikiLink Partial_differential_equation.
- MUSCL_scheme wikiPageWikiLink Riemann_solver.
- MUSCL_scheme wikiPageWikiLink Runge–Kutta.
- MUSCL_scheme wikiPageWikiLink Runge–Kutta_methods.
- MUSCL_scheme wikiPageWikiLink SI.
- MUSCL_scheme wikiPageWikiLink Scalar_(mathematics).
- MUSCL_scheme wikiPageWikiLink Sergei_K._Godunov.
- MUSCL_scheme wikiPageWikiLink Shock_tube.
- MUSCL_scheme wikiPageWikiLink Sod_shock_tube.
- MUSCL_scheme wikiPageWikiLink Spectral_radius.
- MUSCL_scheme wikiPageWikiLink Total_variation_diminishing.
- MUSCL_scheme wikiPageWikiLink Vector_(geometric).
- MUSCL_scheme wikiPageWikiLinkText "MUSCL scheme".
- MUSCL_scheme wikiPageWikiLinkText "MUSCL".
- MUSCL_scheme wikiPageWikiLinkText "Monotonic Upstream-centered Schemes for Conservation Laws".
- MUSCL_scheme hasPhotoCollection MUSCL_scheme.
- MUSCL_scheme wikiPageUsesTemplate Template:Numerical_PDE.
- MUSCL_scheme wikiPageUsesTemplate Template:Reflist.
- MUSCL_scheme subject Category:Computational_fluid_dynamics.
- MUSCL_scheme subject Category:Fluid_dynamics.
- MUSCL_scheme subject Category:Numerical_differential_equations.
- MUSCL_scheme hypernym Method.
- MUSCL_scheme type Software.
- MUSCL_scheme type Dynamic.
- MUSCL_scheme type Mechanic.
- MUSCL_scheme 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).".
- MUSCL_scheme label "MUSCL scheme".
- MUSCL_scheme sameAs m.0f1s0w.
- MUSCL_scheme sameAs Q6719085.
- MUSCL_scheme sameAs Q6719085.
- MUSCL_scheme wasDerivedFrom MUSCL_scheme?oldid=658672232.
- MUSCL_scheme depiction StepFirstOrdUpwind.png.
- MUSCL_scheme isPrimaryTopicOf MUSCL_scheme.
