对流扩散方程的保正守恒特征有限体积法研究

Positivity and Conservative Characteristic Finite Volume Method for Convection Diffusion Equations

本文通过结合特征线方法、保正守恒插值和局部限制器,提出了求解对流占优扩散方程的时空二阶保正守恒特征有限体积法,给出了保正性和守恒性的理论分析。该格式克服了对时间步长的严格限制,所得数值解具有时空二阶精度,且满足保正性和守恒性。数值算例表明了该方法的精度和效果。

In this paper,a temporal and spatial second-order positive and conservative characteristic finite volume method for solving the convection-dominated diffusion equation is proposed by combining the method of characteristics,the positive and conservative interpolation,and local limiter.Positivity and conservativity of the developed method are analyzed theoretically.This scheme overcomes the strict limitation on the time step.The numerical solution has second-order accuracy in space-time,and satisfies positivity and conservation.The accuracy and properties of proposed method are verified by numerical experiments.