High-order boundary conditions for linearized shallow water equations with stratification, dispersion and advection

Abstract

The two-dimensional linearized shallow water equations are considered in unbounded domains with density stratifications. Wave dispersion and advection effects are slso taken into account. The infinite domain is truncated via a rectangular artificial boundary B, and a high-order Open Boundary Condition (OBC) is imposed on B. Then the problem is solved numerically in the finite domain bounded by B. A recently developed boundary scheme is employed, which is based on a reformulation of the sequence of OBC's originaly proposed by Higdon. The OBCs can easily be used up to any desired order. They are incorporated here in a finite difference scheme. Numerical examples are used to demonstrate the performance and advantages of the computational method, with an emphasis on the effect of stratification.