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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 wikiPageRevisionID "604991929".
- MUSCL_scheme hasPhotoCollection MUSCL_scheme.
- MUSCL_scheme subject Category:Computational_fluid_dynamics.
- MUSCL_scheme subject Category:Fluid_dynamics.
- MUSCL_scheme subject Category:Numerical_differential_equations.
- MUSCL_scheme type Abstraction100002137.
- MUSCL_scheme type Communication100033020.
- MUSCL_scheme type DifferentialEquation106670521.
- MUSCL_scheme type Equation106669864.
- MUSCL_scheme type MathematicalStatement106732169.
- MUSCL_scheme type Message106598915.
- MUSCL_scheme type NumericalDifferentialEquations.
- MUSCL_scheme type Statement106722453.
- 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 sameAs MUSCL_scheme.
- MUSCL_scheme wasDerivedFrom MUSCL_scheme?oldid=604991929.
- MUSCL_scheme depiction StepFirstOrdUpwind.png.
- MUSCL_scheme isPrimaryTopicOf MUSCL_scheme.
