A Modified CUI Scheme Based On Hermite Interpolation Polynomials

In this paper,a modified CUI scheme is presented for discretizing the con-vection term.Coupled with Herimite interpolation,CBC(Convection Bounded-ness Criterion)and TVD(Total Variational Diminishing Constraint)are applied to suppress numerical oscillations.This new scheme is a piecewise high reso-lution finite volume numerical scheme.In the second chapter,we provide the specific construction process.The purpose of this paper is to apply the new nu-merical scheme to the convection term in the convection diffusion equation.It is found that the numerical solution of the equation has good accuracy in the s-mooth region,and is stable and bounded near the discontinuity.The scheme can well suppress the non physical oscillations of the numerical solution.The third order Runge-Kutta scheme is used to ensure the high accuracy of the numerical scheme.Typical test cases demonstrate that the present scheme possesses the boundedness of convection and high accuracy.The analytical solution agrees well with the numerical solution near the discontinuity.On the whole,the nu-merical scheme presented in this paper not only keeps the conservation of the finite volume method,but also has high accuracy and good computational sta-bility.