Adaptive finite volume upwind approaches for aeroacoustic computations

The solution-adaptive cell-vertex finite volume upwind approaches on quadrilateral-triangular meshes are presented to solve the unsteady Euler equations. For the present approaches, Runge-Kutta time-integration method, Roe's Riemann solver, a modified area-averaged approach, the MUSCL differencing with two kinds of characteristic interpolation variables, and an improved solution-adaptive technique, where a new mesh-enrichment indicator for acoustic wave is developed, are included, To evaluate the present approaches, Ringleb's flow, transonic flow around the NACA 0012 airfoil, shock propagation in a channel, traveling vortex in a freestream, and an acoustic pulse in a freestream are investigated. In the comparisons of present numerical results with related exact and/or other numerical solutions, it is shown that the upwind approach with the second kind of characteristic variables is accurate and efficient, and the present adaptive technique with appropriate mesh-enrichment indicators enhances this upwind approach to capture the shock wave, vortex, and acoustic wave, By using this solution-adaptive approach to solve the vortex-shock interaction and transonic blade-vortex interaction problems, the flow phenomena and aeroacoustic behaviors are simulated.