Enforcing positivity with conservation for nine-point scheme of nonlinear diffusion equations

The nine-point scheme (NPS) is a finite volume scheme for solving nonlinear diffusion equations on quadrilateral grids. It’s well-known that the solution of the scheme on distorted grids cannot preserve positivity when all given data are nonnegative. Here for the NPS of nonlinear diffusion problems we propose a conservative enforcing positivity algorithm (CEPA), which is posterior correction of the discrete solution, and allows the new solution preserves positivity as well as local conservation at each step of nonlinear iteration. Numerical results are presented to demonstrate that the accuracy of our algorithm of enforcing positivity with conservation is higher than some common procedures of positivity correction.