A Reduced Order Series Expansion for the BEM Incorporating the Boundary Layer Impedance Condition

Abstract

When modeling sound waves in fluids it can be important to include the viscous and thermal losses originating from the fluids’ interaction with boundaries. In the audible frequency range, the thickness of the boundary layers is between a micrometer and a millimeter. As such the viscous and thermal losses are important when simulating the properties of small acoustical devices such as e.g. hearing aids or transducers. However, the inclusion of viscous and thermal losses is a computationally demanding task as it requires a fine discretization of the boundary layer in order to fully capture the complicated physical phenomena happening on the microscale. Recently, there has been developments to ease the computational demands using both the Finite Element Method and the Boundary Element Method, by approximating the losses using the Boundary Layer Impedance (BLI) boundary condition. In this paper, we extend previous developments for multi-frequency analysis using the Reduced Order Series Expansion Boundary Element Method to handle the BLI condition. This model follows a two-step procedure: Using a series expansion to decrease the assembly time of the BEM matrices and a projection to reduce the overall memory consumption of the model. Results from two acoustic interior problems show that the model decreases the total computational time by around 96% while using less than 15% of the memory. For both test setups the limiting factor of the accuracy was the reduction and not the series expansion.