Extensions of Active Flux to arbitrary order of accuracy
| Autor: | Abgrall, Remi, Barsukow, Wasilij |
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| Přispěvatelé: | University of Zurich, Barsukow, Wasilij |
| Rok vydání: | 2023 |
| Předmět: |
2603 Analysis
Numerical Analysis (math.NA) high order methods 10123 Institute of Mathematics 510 Mathematics 65M06 65M08 65M60 76N99 2604 Applied Mathematics Active Flux FOS: Mathematics Mathematics - Numerical Analysis conservation laws 2612 Numerical Analysis 2605 Computational Mathematics 2611 Modeling and Simulation |
| DOI: | 10.5167/uzh-233744 |
| Popis: | Active Flux is a recently developed numerical method for hyperbolic conservation laws. Its classical degrees of freedom are cell averages and point values at cell interfaces. These latter are shared between adjacent cells, leading to a globally continuous reconstruction. The update of the point values includes upwinding, but without solving a Riemann Problem. The update of the cell average requires a flux at the cell interface, which can be immediately obtained using the point values. This paper explores different extensions of Active Flux to arbitrarily high order of accuracy, while maintaining the idea of global continuity. We propose to either increase the stencil while keeping the same degrees of freedom, or to increase the number of point values, or to include higher moments as new degrees of freedom. These extensions have different properties, and reflect different views upon the relation of Active Flux to the families of Finite Volume, Finite Difference and Finite Element methods. |
| Databáze: | OpenAIRE |
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