Contribution
Numerical Approaches to the Solution of Galbrun's Equation
* Presenting author
Abstract:
In recent years, the numerical treatment of differential equations for calculating the propagation of sound in flows has gained significant importance. The increasing computing power and the willingness to employ numerical simulations for primary noise assessment reinforced this trend. While current research focuses on upscaling numerical simulations to larger areas, this work investigates the possibility of solving the Galbrun equation, which still includes numerical challenges with existing approaches. Based on the linearized Euler equations, Galbrun’s equation describes the propagation of sound waves in flow utilizing a Lagrangian displacement instead of the commonly used Eulerian pressure and velocity fluctuation. This concept provides advantages concerning the calculation of fluid-structure couplings. Since classical solutions using the finite element method result in spurious modes, further developments in numerical methods facilitate stable solutions. This presentation introduces energy-based methods describing energy flows across boundaries of different physical domains. Using the Hamiltonian function makes it possible to describe the energy flows between multi-physical systems, stabilizing the numerical treatment of Galbrun’s equation and facilitating possible future applications.