In this paper, the authors discuss the unstructured MUSCL (U-MUSCL) reconstruction scheme, an unstructured-grid extension of the κ -scheme of Van Leer, proposed by Burg for the edge-based discretization. This technique has been widely used in practical unstructured-grid fluid-dynamics solvers, but with confusions (e.g., third-order accuracy with κ = 1 / 2 or κ = 1 / 3 ). This paper clarifies some of these confusions: for example, the U-MUSCL scheme can be third-order accurate in the point-valued solution with κ = 1 / 3 on regular grids for linear equations in all dimensions, and it can be third-order accurate with κ = 1 / 2 as the QUICK scheme in one dimension. It is shown that the U-MUSCL scheme cannot be third-order accurate for nonlinear equations, except a very special case of κ = 1 / 2 on regular simplex-element grids, but it can be an accurate low-dissipation second-order scheme. It is also shown that U-MUSCL extrapolates a quadratic function exactly with κ = 1 / 2 on arbitrary grids, provided the gradient is computed by a quadratic least-squares method. Two techniques are discussed, which transform the U-MUSCL scheme into being genuinely third-order accurate on a regular grid: an efficient flux-reconstruction method and a special source-term quadrature formula for κ = 1 / 2 .


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Resolving Confusions over Third-Order Accuracy of Unstructured MUSCL


    Beteiligte:

    Erschienen in:

    AIAA Journal ; 60 , 3 ; 1415-1439


    Erscheinungsdatum :

    2021-11-30


    Format / Umfang :

    25 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




    RESOLVING CONFUSION OVER THIRD-ORDER ACCURACY OF U-MUSCL

    Padway, Emmett / Nishikawa, Hiroaki | TIBKAT | 2021


    Resolving Confusion Over Third-Order Accuracy of U-MUSCL

    Padway, Emmett / Nishikawa, Hiroaki | AIAA | 2021


    Improved multislope MUSCL reconstruction on unstructured grids for shallow water equations

    Zhao, Jiaheng / Özgen, Ilhan / Liang, Dongfang et al. | DataCite | 2018


    An efficient unstructured MUSCL scheme for solving the 2D shallow water equations

    Hou, Jingming / Liang, Qiuhua / Zhang, Hongbin et al. | DataCite | 2015

    Freier Zugriff

    An improved multislope MUSCL scheme for solving shallow water equations on unstructured grids

    Zhao, Jiaheng / Özgen-Xian, Ilhan / Liang, Dongfang et al. | DataCite | 2018