6533b828fe1ef96bd128788b

RESEARCH PRODUCT

Well-Balanced Adaptive Mesh Refinement for shallow water flows

Pep MuletRosa DonatAnna Martínez-gavaraM. Carmen Martí

subject

Rest (physics)Numerical AnalysisMathematical optimizationSpeedupPhysics and Astronomy (miscellaneous)Shock (fluid dynamics)Computer simulationAdaptive mesh refinementApplied MathematicsComputer Science ApplicationsComputational MathematicsWaves and shallow waterModeling and SimulationApplied mathematicsState (computer science)Shallow water equationsMathematics

description

Well-balanced shock capturing (WBSC) schemes constitute nowadays the state of the art in the numerical simulation of shallow water flows. They allow to accurately represent discontinuous behavior, known to occur due to the non-linear hyperbolic nature of the shallow water system, and, at the same time, numerically maintain stationary solutions. In situations of practical interest, these schemes often need to be combined with some kind of adaptivity, in order to speed up computing times. In this paper we discuss what ingredients need to be modified in a block-structured AMR technique in order to ensure that, when combined with a WBSC scheme, the so-called 'water at rest' stationary solutions are exactly preserved.

yearjournalcountryeditionlanguage
2014-01-01Journal of Computational Physics
https://doi.org/10.1016/j.jcp.2013.09.032