An efficient method for the numerical calculation of viscous effects on transient long waves

Previous studies have shown that the Boussinesq equations can be used to calculate the instantaneous bottom shear stress induced by transient or periodic waves. The bottom friction term occurs as a convolution integral in time in the continuity equation. The exact numerical integration of a convolution integral demands large computational resources, which makes the method less useful for large scale computations. In this paper we explore how the value of the convolution integral can be estimated if we only use the values of the variables in a limited number of time steps, and discuss the accuracy and computational cost of this method.