An improved multislope MUSCL scheme for solving shallow water equations on unstructured grids

Abstract

This paper describes an improved vector manipulation multislope monotone upstream-centred scheme for conservation laws (MUSCL) reconstruction for solving the shallow water equations on unstructured grids. This improved MUSCL reconstruction method includes a bigger stencil for the interpolation and saves time for determining the geometric relations compared to the original vector manipulation method, so it is computationally more efficient and straightforward to implement. Four examples involving an analytical solution, laboratory experiments and field-scale measurements are used to test the performance of the proposed scheme. It has been proved that the proposed scheme can provide comparable accuracy and higher efficiency compared to the original vector manipulation method. With the increase of the number of cells, the advantage of the proposed scheme becomes more apparent.