Applications of a central ENO and AUSM schemes based compressible N-S solver with reconstructed conservative variables. (15th September 2021) - Spinelli, Gregorio Gerardo; Celik, Bayram
Highlights: Temporally and spatially high-order finite-volume solver for compressible flows. Central Essentially Non-Oscillatory scheme for spatial reconstruction of conservative variables. A family of Advection Upstream Splitting Method schemes to compute inviscid fluxes. Strong shock interactions simulated via adaptive mesh refinement. Instability free results for high Mach number flows via the AUSM+M scheme. Abstract: In this study we couple a family of AUSM-flux splitting schemes with the CENO high-order scheme and evaluate the overall performance of the developed in-house solver in terms of modeling the flow physics accurately for a wide range of benchmark problems. The solver uses reconstructed conservative variables. The problems include inviscid and viscous flows that cover low subsonic through transonic and hypersonic regimes. We test the order of accuracy of the implemented CENO scheme by interpolating a smooth spherical cosine function and then calculating the L-norms. The obtained results confirm the consistency between the spatial accuracy and the order of reconstruction up to 5th order. We are able to reach 4th order of accuracy in time by using a Runge-Kutta scheme and thereby we obtain a perfect match with the WENO results available in the literature for the unsteady problem of interaction of a moving vortex with a stationary normal shock. In order to reduce the computational cost of the developed solver and to be able to model more challenging problems, we utilize the advantageous adaptive mesh refinement that allows us to resolve the discontinuities near shocks and slip lines. Our adaptive mesh refinement algorithm is based on a smoothness indicator factor, and allows us to reach the same level of accuracy as the WENO schemes do for the inviscid double Mach reflection problem by using considerably less amount of cells.