Klein-Gordon Equation with Advection on Unbounded Domains Using Spectral Elements and High-Order Non-Reflecting Boundary Conditions
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS
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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.
- Numerical Mathematics
- Fluid Mechanics