The Application of "Embedded Solid" Approaches to Computational Aeroacoustic Problems with Complex Geometries

A number of practical problems in aeroacoustics involve the interaction of acoustic fields and bodies with complex geometries. Numerical simulations of these problems require special treatments of curved boundaries, sharp edges, and moving or deformable objects. A body fitted grid can sometimes be used to transform the physical domain to a computational domain with a Cartesian uniformly distributed grid but this is difficult in general. An unstructured grid can also be used together with either finite element or finite volume schemes. Such schemes usually suffer from the fact that they are mostly low-order and the acoustic waves have to propagate through irregular elements. Both approaches introduce numerical dissipation and dispersion that are not physical.

In an alternative approach, sometimes called the embedded solid approach, a rectangular uniformly distributed Cartesian grid is used in the entire physical domain and the effect of solid objects is simulated by changing the fluid density or by applying a fictitious body force. For example, Chung and Morris, in the Impedance Mismatch Method (IMM), replaced the solid object by a fluid of lower density. In the Brinkman Penalization method, originally developed for flow simulation in porous media, a body force proportional to the local fluid velocity is used to simulate the solid object. A modification to this approach is the virtual surface method, in which the desired body force is calculated through an iterative feedback loop. Forcing the fluid velocity to be zero inside the body can also mimic the presence of a solid. In addition, raising the pressure within the body can be used to obtain reflection characteristics similar to those of a solid body.

The present paper uses the Category 2 workshop problems to investigate the accuracy and field of applicability of the embedded solid approach in computational aeroacoustics problems with complex geometries. The Brinkman Penalization method and an extension to it, which is under development by the authors, are examined.