Three‐dimensional tsunami propagation simulations using an unstructured mesh finite element model

Abstract

AbstractLarge‐scale tsunami propagation simulations from the fault region to the coast are conducted using a three‐dimensional (3‐D) parallel unstructured mesh finite element code (Fluidity‐ICOM). Unlike conventional 2‐D approximation models, our tsunami model solves the full 3‐D incompressible Navier‐Stokes (NS) equations. The model is tested against analytical solutions to simple dispersive wave propagation problems. Comparisons of our 3‐D NS model results with those from linear shallow water and linear dispersive wave models demonstrate that the 3‐D NS model simulates the dispersion of very short wavelength components more accurately than the 2‐D models. This improved accuracy is achieved using only a small number (three to five) of vertical layers in the mesh. The numerical error in the wave velocity compared with the linear wave theory is less than 3% up to kH = 40, where k is the wave number and H is the sea depth. The same 2‐D and 3‐D models are also used to simulate two earthquake‐generated tsunamis off the coast of Japan: the 2004 off Kii peninsula and the 2011 off Tohoku tsunamis. The linear dispersive and NS models showed good agreement in the leading waves but differed especially in their near‐source, short wavelength dispersive wave components. This is consistent with the results from earlier tests, suggesting that the 3‐D NS simulations are more accurate. The computational performance on a parallel computer showed good scalability up to 512 cores. By using a combination of unstructured meshes and high‐performance computers, highly accurate 3‐D tsunami simulations can be conducted in a practical timescale.