A stable dual pairing summation-by-parts method for sediment transport model with well-posed boundary conditions

Abstract

We develop a dual pairing summation-by-parts operator with Godunov flux splitting for the sediment transport model. The required number, location, and form of boundary conditions are determined via the energy method at the continuous level. Stability of the initial boundary value problem is rigorously established. At the discrete level the boundary conditions are weakly enforced via penalty terms. Stability of the numerical model is demonstrated through a discrete energy estimate that mimics the continuous energy. Numerical experiments are conducted to verify the analysis.

References

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