High‐order Higdon‐like boundary conditions for exterior transient wave problems

Abstract

SUMMARYRecently developed non-reflecting boundary conditions are applied for exterior time-dependent wave problems in unbounded domains. The linear time-dependent wave equation, with or without a dispersive term, is considered in an infinite domain. The infinite domain is truncated via an artificial boundary B, and a high-order non-reflecting boundary condition (NRBC) is imposed on B. Then the problem is solved numerically in the finite domain bounded by B. The new boundary scheme is based on a reformulation of the sequence of NRBCs proposed by Higdon. We consider here two reformulations: one that involves high-order derivatives with a special discretization scheme, and another that does not involve any high derivatives beyond second order. The latter formulation is made possible by introducing special auxiliary variables on B. In both formulations the new NRBCs can easily be used up to any desired order. They can be incorporated in a finite element or a finite difference scheme; in the present paper the latter is used. In contrast to previous papers using similar formulations, here the method is applied to a fully exterior two-dimensional problem, with a rectangular boundary.

Klein–Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions

“…It should be noted that van Joolen et al [31] show that any choice of C j is guaranteed to reduce spurious reflection as the order of the NRBC (J) increases. While we omit the details here, the core of this argument is the computation of a so-called reflection coefficient that is a product of J factors, each of which are less than one.…”

A Study of Lateral Boundary Conditions for the NRL's Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS)

“…We have generalized our idea to the linearized SWE with zero mean flow [10,12,13]. We also allowed NRBC on all 4 sides of the lateral boundaries [15]. Later we have added advection and stratification [14,16,17].…”

“…In a series of papers [11]- [15], we have shown how to construct high order non-reflecting boundary conditions (NRBC) on the artificial east boundary.…”

High-order non-reflecting boundary conditions for dispersive waves in polar coordinates using spectral elements

“…It should be noted that van Joolen et al [27] show that any choice of C j is guaranteed to reduce spurious reflection as the order of the NRBC (J) increases. While we omit the details here, the core of this argument is the computation of a so-called reflection coefficient that is a product of J factors, each of which are less than one.…”