Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations

Abstract

In this work, spatial second order positivity preserving characteristic block-centered finite difference methods are proposed for solving convection dominated diffusion problems. By using a conservative piecewise parabolic interpolation with positive constraint, the temporal first order scheme is shown to conserve mass exactly and preserve the positivity property of solution. Taking advantage of characteristics, there is no strict restriction on time steps. The scheme is extended to temporal second order by using a particular extrapolation along the characteristics. To restore solution positivity, a mass conservative local limiter is introduced and verified to keep second order accuracy. Numerical examples are carried out to demonstrate the performance of proposed methods.