Two new implementations of viscous and thermal losses using the boundary element method

The Boundary Element Method (BEM) has shown to be a useful tool in the practical modeling of sound waves with viscous and thermal losses. Until lately, all BEM implementations (threedimensional, two-dimensional and axisymmetrical) made use of finite-difference formulas to calculate tangential first and second derivatives of the surface pressure, which are related to the no-slip condition, the physical condition explaining viscous losses at boundaries.

Recent research has led to two new BEM implementations with losses that avoid the use of finite difference schemes. The first is based on an extra set of tangential derivative Boundary Element equations, resulting in integration kernels requiring nodal C1 continuity. The second makes use, after some coordinate transformations, of the derivatives of the element shape functions to calculate tangential derivatives on the boundary.

The new formulations have been programmed in two- and three-dimensional BEM respectively, and applied to test cases and practical calculations. The paper briefly describes the two new implementations and examines their benefits and drawbacks. For example, they have shown to produce better results in particular test cases and more reliable convergence behavior, but they also require more computational effort.

Results for test cases with losses will be presented and brought forward for discussion.