A new positive finite volume scheme for the two‐dimensional convection‐diffusion equation on deformed meshes is proposed. The approximation of the convective flux is based on some available information of the diffusive flux. The scheme can keep local conservation of normal flux on the cell‐edge and can be used to deal with the case that the diffusive coefficients are discontinuous and anisotropic. In addition, no limiter is introduced. For the unsteady problem, the existence of a solution for the nonlinear discrete system is proved. Numerical results show that the new scheme has second order accuracy and can preserve the positivity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.