Application of Higdon non-reflecting boundary conditions to shallow water models

Abstract

In many applications involving wave propagation, problem domains are often very large or unbounded. A common numerical method used to solve such problems is to truncate the domain via artificial boundaries to form a finite computational domain. To accomplish this, Non-Reflecting Boundary Conditions (NRBC's) which minimize spurious wave reflections are imposed. The quality of the solution strongly depends on the properties of both the NRBC and the wave behavior. This dissertation explores the use of Higdon NRBC's to solve shallow water equations (SWE's) in a dispersive environment. A linearized SWE model is developed that includes stratification and advection effects. Initially a single NRBC is used to truncate a semi-infinite channel. Later four NRBC's are used to restrict an infinite plane. In both cases finite rectangular domains are formed. A scheme developed by Neta and Givoli is used to rapidly discretize high-order Higdon NRBC's. Finite difference methods and are used in all numerical schemes, which are solved explicitly when possible. Results will show that Higdon NRBC's can be used effectively to restrict large rectangular domains when solving SWE's that include the before mentioned effects.