A Block–Interface Approach for High–Order Finite–Difference Simulations of Compressible Flows

The application of the high-order accurate schemes with multi-block domains is essential in problems with complex geometries. Primarily, accurate blockinterface treatment is found to be of significant importance for precisely capturing discontinuities in such complex configurations. In the current study, a conservative and accurate multiblock strategy is proposed and implemented for a highorder compact finitedifference solver. For numerical discretization, the BeamWarming linearization scheme is used and further extended for threedimensional problems. Moreover, the fourthorder compact finitedifference scheme is employed for spatial discretization. The capability of the highorder multiblock approach is then evaluated for the onedimensional flow inside a Shubin nozzle, twodimensional flow over a circular bump, and threedimensional flow around a NACA 0012 airfoil. The results showed a reasonable agreement with the available exact solutions and simulation results in the literature. Further, the proposed block-interface treatment performed quite well in capturing shock waves, even in situations that the location of the shock coincides with block interfaces.