Direct numerical simulation of aeroacoustic sound by volume penalization method

Assessment of immersed boundary method as a tool for direct numerical simulation of aeroacoustic sound

“…The first problem is a basic test; the numerical error due to dyadic mesh refinement is checked; a criterion for the mesh size is also given. The second problem has been studied by several authors (Inoue and Hatakeyama, 2002;Marsden et al, 2005;Lysenkoa et al, 2014;Komatsu et al, 2016); the numerical results obtained by the present method is compared to those obtained by a standard method. The third problem is a test for moving boundaries as the cylinder moves in a static grid system; the results are also compared to those obtained by the present method and a standard method in a frame co-moving with the cylinder.…”

“…The last problem checks applicability to aeroacoustic sound in inviscid flows. For the second and third problems the results by a standard method are available since they are also considered in Komatsu et al (2016).…”

“…5). This problem has been studied by several researchers as a benchmark problem in computational aeroacoustics (Inoue and Hatakeyama, 2002;Marsden et al, 2005;Lysenkoa et al, 2014;Komatsu et al, 2016). The 2D compressible Navier-Stokes equations are solved by the present method.…”

“…Recently, the corrected volume penalization (VP) method has been shown to be able to resolve aeroacoustic sound generated in complex and time-varying geometry with sufficient accuracy (Komatsu et al, 2016;Hattori and Komatsu, 2017). This method is an immersed boundary method of continuous approach based on the VP method for compressible flow developed by Liu and Vasilyev (2007) and modified to satisfy Galilean invariance.…”

“…This method is an immersed boundary method of continuous approach based on the VP method for compressible flow developed by Liu and Vasilyev (2007) and modified to satisfy Galilean invariance. There are still two limitations in the corrected VP method by Komatsu et al (2016): (i) it cannot deal with inviscid flows since the volume penalization imposes no-slip boundary conditions at the surface of the rigid bodies; and (ii) it is difficult, though not impossible (Inoue and Hattori, 1999), to resolve shock waves since the compact scheme (Lele, 1992), which is numerically unstable in the absence of viscosity, is employed.…”