Nonlinear Finite Volume Scheme Preserving Positivity for 2D Convection-Diffusion Equations on Polygonal Meshes

Abstract EN

In this paper, a nonlinear finite volume scheme preserving positivity for solving 2D steady convection-diffusion equation on arbitrary convex polygonal meshes is proposed.

First, the nonlinear positivity-preserving finite volume scheme is developed.

Then, in order to avoid the computed solution beyond the upper bound, the cell-centered unknowns and auxiliary unknowns on the cell-edge are corrected.

We prove that the present scheme can avoid the numerical solution beyond the upper bound.

Our scheme is locally conservative and has only cell-centered unknowns.

Numerical results show that our scheme preserves the above conclusion and has second-order accuracy for solution.