A finite volume-based high order, Cartesian cut-cell method for wave propagation

Computational aeroacoustics requires numerical techniques capable of yielding low artificial dispersion and dissipation to preserve the amplitude and the frequency characteristics of the physical processes. Furthermore, for engineering applications, the techniques need to handle irregular geometries associated with realistic configurations. We address these issues by developing an optimized prefactored compact finite volume (OPC-fv) scheme along with a Cartesian cut-cell technique. The OPC-fv scheme seeks to minimize numerical dispersion and dissipation while satisfying the conservation laws. The cut-cell approach treats irregularly shaped boundaries using divide-and-merge procedures for the Cartesian cells while maintaining a desirable level of accuracy. We assess these techniques using several canonical test problems, involving different levels of physical and geometric complexities. Richardson extrapolation is an effective tool for evaluating solutions of no high gradients or discontinuities, and is used to evaluate the performance of the solution technique. It is demonstrated that while the cut-cell method has a modest effect on the order of accuracy, it is a robust method. The combined OPC-fv scheme and the Cartesian cut-cell technique offer good accuracy as well as geometric flexibility.