High Order Difference Method for Low Mach Number Aeroacoustics

The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. While the conventional central sixth-order accurate stencil is employed in the interior, the difierence method is third- order accurate at the boundary to satisfy the summation by parts property analogous to the integration by parts in the continuous energy estimate. Since thereby a discrete energy estimate is automatically satisfled, strict stability of the high order difierence method is guaranteed. The boundary conditions are implemented by a penalty term. The classical Runge-Kutta method is used for time integration. Spurious oscillations are suppressed by a new characteristic-based fllter. The method has been applied to simulate vortex sound at low Mach numbers. The computed acoustic pressure generated by an almost circular Kirchhofi vortex is in excellent agreement with the analytical solution.

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