A High Order Oscillation-free Finite Volum Method For Nonlinear Coupled Equations

In the study of nonlinear wave phenomena,the solution of nonlinear development equation has drawn widely attention.This paper introduces two classes of coupled nonlinear development equation: coupled Burgers equation and coupled KdV equation.It's always difficult to get the exact solution because of their complexity.So scholars began to study their numerical solution.In the past,most of the researches were focused on a single nonlinear development equation.Because the characteristics of the coupled nonlinear development equations lie in their nonlinearity and coupling,the existing numerical methods generally have a large amount of computation and their calculation accuracy and stability need to be further optimized.Among many numerical methods of Partial Differential Equations,the physical meaning of Finite Volume Method is relatively intuitive and clear.Moreover,it's calculation accuracy and calculation complexity are moderate,and the calculation principle is local conservation,which is suitable for solving the flow field with complex boundary,so it is widely used in Computational Fluid Dynamics.This paper solves two classes of coupled nonlinear equations based on finite volume in a uniform grid.A new scheme for discretizing convective term is constructed by Hermite interpolation method with satisfying CBC and TVD criterion,and the time discretization is fulfilled by using the third order Runge-Kutta scheme.It is verified that this scheme has gained a good computational performance by several numerical examples.