A Frequency Domain Immersed Boundary Method and its Application to 2-dimensional Acoustic Problems

Abstract

A frequency domain Immersed Boundary (IB) method was developed and validated in the present paper using 2-dimenstional acoustical radiation and scattering cases. The IB method was incorporated with Linearized Euler Equations (LEE) in the frequency domain in the present work. The governing equations were spatially discretisized using the DRP scheme. A pseudo time dependant term was added to the frequency domain equations, allowing the use of a conventional time-marching algorithm to converge the solutions in the pseudo-time domain. Perfectly Matched Layers (PML) were placed at boundaries of computational domain where non-reflective conditions were expected. PML technique was also implemented inside the rigid body to stabilize the computation. The impermeable boundary condition on the surface of the geometry is guaranteed by finding the inverse of an influence matrix, which establishes the relationship between boundary forces and induced velocity. Numerical computations were performed for 2-dimensional acoustic radiation and scattering problems. Computational results were compared with exact solution and yielded good agreement, providing a solid validation of the current method. The method is expected to extend to higher dimension and applied to more complex problem like wake/airfoil interaction simulations in turbomachinery.