Unstructured high-order galerkin-temporal-boundary methods for the klein-gordon equation with non-reflecting boundary conditions

摘要

A reduced shallow water model under constant, non-zero advection in infinite domains is considered. High-Order Givoli-Neta (G-N) and Hagstrom-Hariharan (H-H) non-reflecting boundary conditions (NRBCs) are introduced 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 discretizations. Several alternatives are also presented for solving open domain problems. These alternatives include adjustments to the G-N NRBC based on physical arguments as well as formulating the boundary condition for arbitrary domains using unstructured grids. The H-H polar NRBC is also formulated in an unstructured grid setting and extended to include dispersive effects. Results show that by balancing all numerical errors involved, high-order accuracy can be achieved for unbounded channel problems. Further, the adjustments to the G-N and H-H NRBCs to operate in an unstructured grid setting are shown to significantly reduce errors over first order non-reflecting boundary schemes when operating in an open domain configuration.