A Roe-related semi-Lagrangian method

An algorithm for 1D and 2D Euler equations was proposed by combining the Roe scheme and the semi-Lagrangian method based on characteristic theory. The finite volume method (FVM) is cast in a flux form and thus guarantees the numerical conservation. We calculated the flux at the cell boundary by using its value at the boundary's center, which could make the algorithm second-order accuracy in time. The semi-Lagrangian method with characteristic theory was implemented to trace the fluid particles. The characteristic velocities were modified based on Roe average to locate the departure points. The interpolation by ENO reconstruction made the algorithm free of limiters. The high order algorithm is simple and convenient to implement. The numerical results showed that it was competitive comparing with other schemes.