Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations (Advances in Applied Mathematics and Mechanics, 2022)
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 andpreserve the positivity property of solution. Taking advantage of characteristics, thereis no strict restriction on time steps. The scheme is extended to temporal second order by using a particular extrapolation along the characteristics. To restore solutionpositivity, a mass conservative local limiter is introduced and verified to keep secondorder accuracy. Numerical examples are carried out to demonstrate the performanceof proposed methods.