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High-order, finite-volume methods in mapped coordinates
- Source :
- Journal of Computational Physics. 230:2952-2976
- Publication Year :
- 2011
- Publisher :
- Elsevier BV, 2011.
-
Abstract
- 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.
- Subjects :
- 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
Subjects
Details
- ISSN :
- 00219991
- Volume :
- 230
- Database :
- OpenAIRE
- Journal :
- Journal of Computational Physics
- Accession number :
- edsair.doi...........b4d0d5b706840765695f1e21773a6f7c