Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation
The problem of modelling unidirectional propagation of weakly nonlinear, long waves in the presence of dispersion, among other things, is governed by the Benjamin-Bona-Mahony (BBM) equation. Normally, it is considered as an alternative to the Korteweg-de Vries equation, due to some of its analytical advantages. The authors study the linearized BBM equation. First, the continuous transparent boundary conditions are presented for the linearized BBM equation. Two accurate space and time discretizations of this equation are proposed and the process of deriving the discrete transparent boundary conditions is given. The consistency of the discrete transparent boundary conditions with the continuous ones is proved. The convergence of the numerical scheme relying on a stability analysis is also shown. Three types of numerical simulation are performed to illustrate the findings of the work.
discrete transparent boundary conditions
scientific article; zbMATH DE number 6894071
scientific article