Conservative and Oscillationless Semi-Lagrangian Schemes for Tsunami Modelling

Abstract

In this paper, we applied and evaluated the performance of a higher-order scheme based on volume/surface integrated average based multi-moment method (VSIAM3) for the simulation of tsunami propagation on land. The advection term in the momentum equation was solved by using the conservative semi-Lagrangian scheme with third-order accuracy based on constrained interpolation profile (CIP–CSL3). In order to reduce the numerical diffusion and suppress the numerical oscillation, we adopted the Collela-Woodward (CW) reconstruction method to approximate the slope in the CIP–CSL3 interpolation function. The moving interface between air-water was captured by using the volume of fluid (VOF) method. We opted for the algebraic type of VOF to avoid geometrical surface reconstruction difficulty, where the tangent of hyperbola for interface capturing (THINC) scheme was used to compute a sharp and smear-less air-water interface. We first compared the validity and stability of our two-dimensional numerical model by conducting a numerical test with dam-break flow problem. Results were excellent in terms of the front propagation speed (3% slower than physical experiment). Our numerical model was then applied to simulate tsunami propagation on land and the results were compared to the hydraulic experimental results as well as the numerical results of a proprietary software (FLOW-3D). The results demonstrated an improvement of the flow surface resolution and a better wave arrival prediction as compared to the FLOW-3D model. The accuracy of maximum pressure estimation was also improved by as much as 5% through the upgrade of the original first-order gradient approximation to the higher-order CW method in the CIP-CSL3 interpolation.