A cell-centered spatiotemporal coupled method for the compressible Euler equations

A cell-centered spatiotemporal coupled method is developed to solve the compressible Euler equations. The spatial discretization is performed using an improved weighted essentially non-oscillation scheme, where the Harten-Lax-van Leer-contact approximate Riemann solver is used for computing the numerical fluxes. A two-stage fourth-order scheme is adopted to carry out time advancement for unsteady problems. The proposed method is featured by spatiotemporal coupling time-stepping that can be generalized without using the case-dependent generalized Riemann problem solver. A number of one- and two-dimensional test cases are presented to demonstrate the performance of the proposed method for solving the compressible Euler equations on structured grids. The numerical results indicate that the novel method can achieve relatively large Courant-Friedrichs-Lewy (CFL) number compared to other studies that implement the two-stage fourth-order scheme, and that it is more capable of capturing small-scale flow structures than the Runge-Kutta (RK) method.