Lighthill’s inhomogeneous wave equation for high Mach numbers
* Presenting author
Abstract:
Lighthill’s famous analogy reformulates the compressible flow equations into an inhomogeneous wave equation exactly. In doing so, the wave operator with the density fluctuation as solution variable does not include any interaction between flow and wave structures. All nonlinearities and interactions are combined into the right-hand side being the second spatial derivative of Lighthill’s tensor including the Reynolds stresses, the excess of momentum transfer, and the viscous stress tensor. Although the numerical solution of this inhomogeneous wave equation can be performed efficiently, it first needs the results of the whole set of compressible flow dynamics equations to be able to calculate Lighthill’s tensor. Despite this challenge, Lighthill’s analogy might be an attractive approach even for confined flows as, e.g., turbocharger noise. In this contribution, we will discuss in detail the physical/mathematical prerequisites for this two-step approach: (1) Compressible flow computation on a restricted domain; (2) Solving Lighthill’s inhomogeneous wave equation by the Finite Element (FE) method on a larger domain.