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Numerical assessment of criteria for mesh adaptation in the finite volume solution of shallow water equations. (English) Zbl 1488.65343

Summary: We present a numerical assessment of a class of criteria for mesh adaptation in the finite volume solution of shallow water flows. The shallow water equations are numerically approximated by a predictor-corrector procedure in unstructured triangular meshes. The numerical fluxes at the interfaces of each triangle are reconstructed in the predictor stage using an upwind scheme along with slope limiters to achieve a second-order accuracy. Treatment of source terms is performed in the corrector stage using a well-balanced technique. Four error indicators using the flow variables are discussed and applied as criteria for the mesh adaptation. Numerical results are presented for two test examples for a circular dam-break flow and dam-break problem over a single building. The presented criteria are found to give accurate results in comparison with similar simulations carried out using uniformly refined fixed meshes. Dynamic grid adaptation and the use of an explicit time integration scheme are found to enhance the computational efficiency of the finite volume solution of shallow water flows. In addition, the obtained results for dam-break problems are considered to be representative, and might be helpful for a fair rating of criteria for mesh adaptation in the finite volume solution of shallow water flows, particularly in long time computations.

MSC:

65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65L05 Numerical methods for initial value problems involving ordinary differential equations
65N08 Finite volume methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35L53 Initial-boundary value problems for second-order hyperbolic systems
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
74J40 Shocks and related discontinuities in solid mechanics
76B07 Free-surface potential flows for incompressible inviscid fluids

Software:

GEOCLAW; ADER-DG
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Full Text: DOI

References:

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