Premium
A second‐order radiation boundary condition for the shallow water wave equations on two‐dimensional unstructured finite element grids
Author(s) -
Johnsen Matthias,
Lynch Daniel R.
Publication year - 1994
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650180604
Subject(s) - mathematics , polygon mesh , finite element method , mathematical analysis , boundary value problem , curvature , galerkin method , boundary (topology) , wave equation , discontinuous galerkin method , singular boundary method , boundary knot method , geometry , boundary element method , physics , thermodynamics
A second‐order radiation boundary condition (RBC) is derived for 2D shallow water problems posed in ‘wave equation’ form and is implemented within the Galerkin finite element framework. The RBC is derived by matching the dispersion relation for the interior wave equation with an approximate solution to the exterior problem for outgoing waves. The matching is correct to second order, accounting for curvature of the wave front and the geometry. Implementation is achieved by using the RBC as an evolution equation for the normal gradient on the boundary, coupled through the natural boundary integral of the Galerkin interior problem. The formulation is easily implemented on non‐straight, unstructured meshes of simple elements. Test cases show fidelity to solutions obtained on extended meshes and improvement relative to simpler first‐order RBCs.