A Domain Decomposition Method for Linearized Boussinesq-Type Equations (Journal of Mathematical Study, 2019)
In this paper, we derive discrete transparent boundary conditions for a classof linearized Boussinesq equations. These conditions happen to be non-local in timeand we test numerically their accuracy with a Crank-Nicolson time-discretization ona staggered grid. We use the derived transparent boundary conditions as interfaceconditions in a domain decomposition method, where they become local in time. Weanalyze numerically their efficiency thanks to comparisons made with other interfaceconditions.
Keywords: Boussinesq-type equations; finite differences scheme; transparent boundary conditions; domain decomposition; interface conditions; Schwarz alternating method.