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- High-resolution_scheme abstract "High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following properties:Second or higher order spatial accuracy is obtained in smooth parts of the solution.Solutions are free from spurious oscillations or wiggles.High accuracy is obtained around shocks and discontinuities.The number of mesh points containing the wave is small compared with a first-order scheme with similar accuracy.General methods are often not adequate for accurate resolution ofsteep gradient phenomena; they usually introduce non-physical effectssuch as smearing of the solution or spurious oscillations.Since publication of Godunov's order barrier theorem, whichproved that linear methods cannot provide non-oscillatory solutionshigher than first order (Godunov-1954, Godunov-1959), these difficultieshave attracted a lot of attention and a number of techniques havebeen developed that largely overcome these problems. To avoid spuriousor non-physical oscillations where shocks are present, schemes thatexhibit a Total Variation Diminishing (TVD) characteristicare especially attractive.Two techniques that are proving to be particularlyeffective are MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws)a flux/slope limiter method (van Leer-1979, Hirsch-1990,Tannehill-1997, Laney-1998, Toro-1999) andthe WENO (Weighted Essentially Non-Oscillatory) method (Shu-1998, Shu-2009). Both methodsare usually referred to as high resolution schemes (see diagram).MUSCL methods are generally second-order accurate in smooth regions (althoughthey can be formulated for higher orders) and provide good resolution,monotonic solutions around discontinuities. They are straight-forwardto implement and are computationally efficient.For problems comprisingboth shocks and complex smooth solution structure, WENO schemes canprovide higher accuracy than second-order schemes along with goodresolution around discontinuities. Most applications tend to use afifth order accurate WENO scheme, whilst higher order schemes canbe used where the problem demands improved accuracy in smooth regions.".
- High-resolution_scheme thumbnail MUSCL_HiRes.jpg?width=300.
- High-resolution_scheme wikiPageID "5679554".
- High-resolution_scheme wikiPageLength "4340".
- High-resolution_scheme wikiPageOutDegree "13".
- High-resolution_scheme wikiPageRevisionID "645883966".
- High-resolution_scheme wikiPageWikiLink Category:Computational_fluid_dynamics.
- High-resolution_scheme wikiPageWikiLink Category:Numerical_differential_equations.
- High-resolution_scheme wikiPageWikiLink Flux_limiter.
- High-resolution_scheme wikiPageWikiLink Godunovs_theorem.
- High-resolution_scheme wikiPageWikiLink MUSCL_scheme.
- High-resolution_scheme wikiPageWikiLink Order_of_accuracy.
- High-resolution_scheme wikiPageWikiLink Partial_differential_equation.
- High-resolution_scheme wikiPageWikiLink Partial_differential_equations.
- High-resolution_scheme wikiPageWikiLink Sergei_K._Godunov.
- High-resolution_scheme wikiPageWikiLink Shock_capturing_method.
- High-resolution_scheme wikiPageWikiLink Shock_capturing_methods.
- High-resolution_scheme wikiPageWikiLink Total_Variation_Diminishing.
- High-resolution_scheme wikiPageWikiLink Total_variation_diminishing.
- High-resolution_scheme wikiPageWikiLink File:MUSCL_HiRes.jpg.
- High-resolution_scheme wikiPageWikiLinkText "High-resolution scheme".
- High-resolution_scheme wikiPageWikiLinkText "high-order numerical schemes".
- High-resolution_scheme wikiPageWikiLinkText "high-resolution scheme".
- High-resolution_scheme wikiPageWikiLinkText "high-resolution".
- High-resolution_scheme hasPhotoCollection High-resolution_scheme.
- High-resolution_scheme wikiPageUsesTemplate Template:Numerical_PDE.
- High-resolution_scheme subject Category:Computational_fluid_dynamics.
- High-resolution_scheme subject Category:Numerical_differential_equations.
- High-resolution_scheme type Dynamic.
- High-resolution_scheme comment "High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities.".
- High-resolution_scheme label "High-resolution scheme".
- High-resolution_scheme sameAs m.0dzrp9.
- High-resolution_scheme sameAs Q17029736.
- High-resolution_scheme sameAs Q17029736.
- High-resolution_scheme wasDerivedFrom High-resolution_scheme?oldid=645883966.
- High-resolution_scheme depiction MUSCL_HiRes.jpg.
- High-resolution_scheme isPrimaryTopicOf High-resolution_scheme.