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This paper presents a space-time stabilized finite element method for shallow water flow considering moving boundaries. The finite element method is introduced for both space and time discretization to express the moving boundaries, accurately. The SUPG formulation is employed for the finite element discretization, and the shock capturing method is introduced to remove the numerical instability at the free surface. A new stabilized parameter for shock capturing term and the adaptive remeshing technique are introduced to improved the numerical accuracy. The present method is applied to several numerical test examples and the computed results are compared with the existing analytical and experimental results.

A Space-Time Stabilized Finite Element Method using Mesh Refinement Method for Shallow Water Flow Considering Moving Boundaries