An Eulerian-Lagrangian Runge-Kutta finite volume (EL-RK-FV) method for solving convection and convection-diffusion equations

We propose a new Eulerian-Lagrangian Runge-Kutta finite volume method for numerically solving convection and convection-diffusion equations. semi-Lagrangian methods have grown in popularity mostly due to their ability allow large time steps. Our proposed scheme is formulated by integrating the PDE on space-time region partitioned approximations of characteristics determined from Rankine-Hugoniot jump condition; then rewriting time-integral form into differential application (RK) via method-of-lines approach. The can be viewed as generalization standard (RK-FV) which approximate with zero velocity. high-order spatial reconstruction achieved using recently developed weighted essentially non-oscillatory schemes adaptive order (WENO-AO); temporal accuracy explicit RK equations implicit-explicit (IMEX) algorithm extends higher dimensions dimensional splitting. Numerical experiments demonstrate our algorithm's robustness, accuracy, handle extra