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• W3048953333 abstract "Presently, an approximate delta function (ADF) is defined in multi-dimensional space in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand spanning a finite domain. By using this ADF over a two-dimensional unstructured mesh, a compact high-order point-value enhanced finite volume method (PFV) is constructed. The corresponding scheme is capable of storing and updating cell-averaged values inside each element as well as the unknown quantities and their derivatives (when needed) on vertex points. The sharing of vertex information with surrounding elements reduces the number of degrees of freedom relative to other compact and high-order methods of comparable convergence rate. To ensure conservation, cell-averaged values are updated using an identical approach to the one traditionally followed in the finite volume method. To verify the performance of the PFV scheme at successive orders, its accuracy and stability are vetted using benchmark problems associated with the two-dimensional wave and Euler equations encompassing a total of six standard test cases." @default.
• W3048953333 created "2020-08-18" @default.
• W3048953333 creator A5045768438 @default.
• W3048953333 creator A5056903809 @default.
• W3048953333 date "2020-12-01" @default.
• W3048953333 modified "2023-09-28" @default.
• W3048953333 title "High-order point-value enhanced finite volume method for two-dimensional hyperbolic equations on unstructured meshes" @default.
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• W3048953333 doi "https://doi.org/10.1016/j.jcp.2020.109756" @default.
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