Numerical Simulation of Tsunami Run-Up

SYNOPSISA linear set of equations of long waves in the Lagrangian description is solved numerically to obtain run-up heights on lands of arbitrary shape. As the water depth and the land elevation vary from place to place, the resulted equations have coefficients which vary depending upon topography. However, it is shown that the CFL criterion provides a stability condition. A false coundary is introduced to complete the computational molecule at the wave front. Numerical results are compared with theoretical ones in case of a simple topography and the agreement is quite satisfactory. Although only the one-dimensional problems are treated in the paper, extension to the two-dimensional case has no difficulty in principle.