Direct numerical simulation of aeroacoustic sound by volume penalization method

The volume penalization (VP) method for compressible flows is investigated as a tool of direct numerical simulation of aeroacoustic sound in problems where not only acoustic pressure but also hydrodynamic pressure depends on time and position. First, it is shown that the method proposed by Liu and Vasilyev (2007) [30] is not Galilean invariant. It is corrected to satisfy Galilean invariance. Next, numerical accuracy of the corrected VP method is investigated in problems of simple geometry which can be simulated also by a standard method on a body-fitted coordinate system: sound generation in (i) flow past a fixed square/circular cylinder, (ii) flow past an oscillating square/circular cylinder, and (iii) flow past two square cylinders. The results confirm that the corrected VP method gives reasonably accurate results for sound pressure which is much smaller than hydrodynamic pressure within 5% error. Finally, the corrected method is applied to two examples of complex geometry, which cannot be simulated by standard methods using body-fitted coordinate systems without considerable difficulty: sound generation in (i) flow past an oscillating cylinder and a fixed cylinder behind it and (ii) flow past a bundle of cylinders. The results show that the present method is in principle applicable to aeroacoustic problems in any complex geometry including practical engineering ones.