A Kinetic Flux-vector Splitting Scheme for Two-layer Shallow Flow Model

In this article, two-layer shallow flow model with non-flat basal topography is considered. The presence of coupling terms in two layers make the system conditional hyperbolic. The kinetic flux-vector splitting (KFVS) scheme is applied to approximate the corresponding one-dimensional two-layer shallow flow equations. Our interest lies in the numerical approximation of the model referred to above, the complexity of which poses numerical problems. The higher order accuracy of the scheme is achieved by using a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is able to treat variety of flow conditions. A number of test cases are carried out to verify the performance of the suggested method. The conservation and solution element (CESE) scheme is used for comparison. It is observed from the comparison that KFVS resolves the shocks more effectively than CESE scheme.

Keywords:

Two-layer SWEs , KFVS scheme , CESE , non-flat bottom topography , discontinuous solutions , conservation laws‎