Symmetry-preserving finite-difference discretizations of arbitrary order on structured curvilinear staggered grids
| Autor: | Mathea J. Vuik, Bas van 't Hof |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Curvilinear coordinates
General Computer Science Discretization Continuous modelling Finite difference Numerical Analysis (math.NA) 02 engineering and technology 01 natural sciences Symmetry (physics) 010305 fluids & plasmas Theoretical Computer Science Nonlinear system Rate of convergence Modeling and Simulation 0103 physical sciences FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Applied mathematics 020201 artificial intelligence & image processing Mathematics - Numerical Analysis Boundary value problem Mathematics |
| Zdroj: | Journal of Computational Science. 36:101008 |
| ISSN: | 1877-7503 |
| DOI: | 10.1016/j.jocs.2019.06.005 |
| Popis: | Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and energy are proven in the same way as for the original continuous model. This paper presents a new finite-difference symmetry-preserving space discretization. Boundary conditions and time integration are not addressed. The novelty is that it combines arbitrary order of convergence, orthogonal and non-orthogonal structured curvilinear staggered meshes, and the applicability to a wide variety of continuous operators, involving chain rules and nonlinear advection, as illustrated by the shallow-water equations. Experiments show exact conservation and convergence corresponding to expected order. |
| Databáze: | OpenAIRE |
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