CONSTRUCTION OF NONLINEAR WEIGHTED METHOD FOR FINITE VOLUME SCHEMES PRESERVING MAXIMUM PRINCIPLE

For the construction of finite volume schemes preserving maximum principle for diffusion equations on distorted meshes, the nonlinear weighted method has become a commonly used approach. In this paper we present three finite volume schemes preserving maximum principle based on nonlinear weighted methods, in which a conservative flux is constructed by using three kinds of weighted combination of nonconservative flux. We perform an elementary analysis to compare the errors of flux for these weighted methods, which shows that Scheme 3 is the best of the three schemes. Moreover, we propose a general approach to construct the nonlinear weighted method. Numerical results are presented to demonstrate the accuracy and properties of these schemes.