Transparent boundary conditions for the linearized Benjamin-Bona-Mahony equation (Christophe Besse, Toulouse)

26.04.2016 14:15

The Benjamin-Bona-Mahony (BBM) equation is a classical nonlinear, dispersive equation which model the unidirectional propagation of weakly nonlinear, long waves in the presence of dispersion. It is usually proposed as an analytically advantageous alternative to the well-known Korteweg-de Vries equation. We consider various approximations of transparent boundary conditions (TBC) for linearized BBM equation. In this talk, we derive explicit TBCs both continuous and discrete for the linearized BBM equation. The equation is discretized with the Crank Nicolson time discretization scheme and we focus on the difference between the upwind and the centered discretization of the convection term. We use these boundary conditions to compute solutions with compact support in the computational domain and also in the case of an incoming plane wave which is an exact solution of the linearized BBM equation.

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