일차원 고차 Boussinesq 방정식에 대한 불연속 갤러킨 유한요소법의 적용

Application of DGFEM to 1D High-Order Boussinesq Equation

The Runge-Kutta DGFEM (Discontinuous Galerkin Finite Element Method) is applied to the discretization of 1D high-order Boussinesq equation of Madsen et al. (2002). Discontinuous Galerkin method is used, which allows discontinuities at the element interfaces, for the spatial discretization and explicit high-order Runge-Kutta method is adopted in time integration. The connection between interfaces is set as an approximate Riemann problem and Lax-Friedrichs numerical fluxes are employed. To remove the unnecessary oscillations, Savitzky-Golay filter is applied to the solution at each time step. When necessary, a numerical sponge layer is set to mimic the open boundary condition and relaxation zone is set for the internal wave generation. As benchmark case studies, the propagation of sine (linear) wave and nonlinear wave over a submerged breakwater are simulated with the developed numerical model. For the latter case study, the results are compared with experimental data and good agreement is observed.