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

A reduced shallow water model under constant, non-zero advection in the infinite channel is considered. High-order (Givoli-Neta) non-reflecting boundary conditions are introduced in various configurations to create a finite computational space and solved using a spectral element formulation with high-order time integration. Numerical examples are used to demonstrate the synergy of using high-order spatial, time, and boundary discretization. We show that by balancing all numerical errors involved, high-order accuracy can be achieved for unbounded domain problems.