A Backward-Characteristics Monotonicity Preserving Method for Stiff Transport Problems

Convection-diffusion problems in highly convective flows can exhibit complicated features such as sharp shocks and shear layers which involve steep gradients in their solutions. As a consequence, developing an efficient computational solver to capture these flow features requires the adjustment of the local scale difference between convection and diffusion terms in the governing equations. In this study, we propose a monotonicity preserving backward characteristics scheme combined with a second-order BDF2-Petrov-Galerkin finite volume method to deal with the multiphysics nature of the problem. Unlike the conventional Eulerian techniques, the two-step backward differentiation procedure is applied along the characteristic curves to obtain a second-order accuracy. Numerical results are presented for several benchmark problems including sediment transport in coastal areas. The obtained results demonstrate the ability of the new algorithm to accurately maintain the shape of the computed solutions in the presence of sharp gradients and shocks.