High-order, finite-volume methods in mapped coordinates
| Autor: | Phillip Colella, Jeffrey Hittinger, Daniel F. Martin, M. R. Dorr |
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| Rok vydání: | 2011 |
| Předmět: |
Numerical Analysis
Partial differential equation Finite volume method Physics and Astronomy (miscellaneous) Discretization Applied Mathematics Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Order of accuracy Computer Science Applications law.invention Quadrature (mathematics) Computational Mathematics law Modeling and Simulation Cartesian coordinate system Coordinate space Hyperbolic partial differential equation Mathematics |
| Zdroj: | Journal of Computational Physics. 230:2952-2976 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2010.12.044 |
| Popis: | We present an approach for constructing finite-volume methods for flux-divergence forms to any order of accuracy defined as the image of a smooth mapping from a rectangular discretization of an abstract coordinate space. Our approach is based on two ideas. The first is that of using higher-order quadrature rules to compute the flux averages over faces that generalize a method developed for Cartesian grids to the case of mapped grids. The second is a method for computing the averages of the metric terms on faces such that freestream preservation is automatically satisfied. We derive detailed formulas for the cases of fourth-order accurate discretizations of linear elliptic and hyperbolic partial differential equations. For the latter case, we combine the method so derived with Runge-Kutta time discretization and demonstrate how to incorporate a high-order accurate limiter with the goal of obtaining a method that is robust in the presence of discontinuities and underresolved gradients. For both elliptic and hyperbolic problems, we demonstrate that the resulting methods are fourth-order accurate for smooth solutions. |
| Databáze: | OpenAIRE |
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