CHARACTERISTICS AND INFLUENCE OF THE NUMERICAL INSTABILITY ON FINITE-DIFFERENCE ANALYSIS OF TSUNAMIS BASED ON NONLINEAR SHALLOW WATER THEORY

Abstract

 The relationship between two discretization methods and tsunami behavior for finite-difference simulations of tsunamis based on nonlinear shallow water theory is analyzed. Methods for determining whether a tsunami waveform contains numerical oscillations are investigated. It is shown that short-period oscillations that affect the maximum tsunami elevation appear as a result of numerical instability caused by steepening of the wavefront. It is also shown that the magnitude of the numerical viscosity caused by the truncation error associated with the discretization of the governing equation has a strong correlation with general nonlinear indices. Furthermore, the effect of the local viscosity term to effectively suppress the oscillations is verified.