A positivity-preserving high order discontinuous Galerkin scheme for convection–diffusion equations
| Autor: | Sashank Srinivasan, Xiangxiong Zhang, Jonathan Poggie |
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| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Scalar (physics) 010103 numerical & computational mathematics 01 natural sciences Parabolic partial differential equation Computer Science Applications 010101 applied mathematics Computational Mathematics Nonlinear system Discontinuous Galerkin method Modeling and Simulation Neumann boundary condition Periodic boundary conditions Applied mathematics 0101 mathematics Diffusion (business) Convection–diffusion equation Mathematics |
| Zdroj: | Journal of Computational Physics. 366:120-143 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2018.04.002 |
| Popis: | For constructing high order accurate positivity-preserving schemes for convection–diffusion equations, we construct a simple positivity-preserving diffusion flux. Discontinuous Galerkin (DG) schemes with such a positivity-preserving diffusion flux are nonlinear schemes, which can be regarded as a reduction of the high order positivity-preserving DG schemes for compressible Navier–Stokes equations in [1] to scalar diffusion operators. In this paper we focus on the local DG method to discuss how to apply such a flux. A limiter on the auxiliary variable for approximating the gradient of the solution must be used so that the diffusion flux is positivity-preserving in the sense that DG schemes with this flux satisfies a weak positivity property. Together with a positivity-preserving limiter, high order DG schemes with strong stability preserving time discretizations can be rendered positivity-preserving without losing conservation or high order accuracy for convection–diffusion problems with periodic boundary conditions or a special class of Dirichlet or Neumann boundary conditions. Numerical tests on a few parabolic equations and an application to modeling electrical discharges are shown to demonstrate the performance of this scheme. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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