Application of the random choice method to shallow water equations

Abstract

The Random Choice Method is applied to the one-dimensional shallow water equations with operational splitting to take into account forced domain motion. The Random Choice Method is based on randomly sampling exact Riemann solutions and thus the Riemann solution for the shallow water equations plays a key role in applying the method. The details of the application are presented and the methods accuracy and applicability is discussed through comparison to experimental results as well as literature review. Furthermore, the possible extension of the method to two dimensions is discussed. Since much of the physics of the flow is neglected in assumptions made in the derivation of the shallow water equations, it is clear that phenomena such as wave breaking and turbulence effects can not be captured with the method. However, the results obtained here show that the method can be applied to solve the shallow water motion under domain excitation, as long as the excitation frequency is relatively low. With higher frequencies of excitation the results show error in the conservation of mass.