A High Resolution NV/CBC Finite Volume Scheme For The Generalized Regularized Long Wave Equation

An oscillation-free high order scheme is presented for the generalized long wave equation by using the normalized-variable formulation in the finite volume framework. The exact solution of the generalized long wave equation is usually difficult to solve. Consequently, to solve its numerical solution is an important method for study at present. The aim of this paper is to reconstruction a numerical scheme to approach the exact of the generalized long wave equation. The numerical scheme in this paper adopts the QUICK finite volume scheme as the basic scheme to obtain high order accuracy in smooth solution domain. In order to suppress non-physical oscillations of numerical solutions by high order linear schemes, the CBC (convection boundedness criterion) condition is combined with the TVD (total variation diminishing) constraint in the normalized variable formulation to design a bounded QUICK scheme. For time discretization, a stable 3rd order Runge-kutta scheme is used in order to assure high order accuracy globally. Finally, take modified regularized long wave and regularized long wave for examples and several numerical experiments are performed, including the motion of single solitary wave, collision of two solitary waves, development of the Maxwellian initial condition, generation of wave undulation tests. Numerical results demonstrate that the present scheme possesses good robustness and high resolution.