CSE Community Seminar
April 11, 2025, 12-1PM
Conference Room 45-432 in Building 45
On the Application of an Output-based Adaptive, Higher-order Finite Element Method to Sonic Boom Propagation
Renato Trono Figueras
PhD Student, Department of Aeronautics and Astronautics, MIT
Abstract:
The ability to accurately predict the evolution of sonic booms from the nearfield of a supersonic airplane through the atmosphere and compute the corresponding loudness levels at ground is a key step in the broader objective of airplane shape optimization. The seminar describes a loudness-based adaptive, higher-order finite element method for sonic boom propagation. Unlike time-marching schemes, our space-time method allows fully-unstructured mesh adaptation and thus a more efficient usage of degrees of freedom. The boom propagation is modeled using the augmented Burgers system of equations, including effects of thermoviscous diffusion, species relaxation, a stratified atmosphere, and ray tube area variation. In addition, we employ a PDE-based shock wave sensor to add artificial viscosity in shock areas, allowing to capture shocks and have better numerical stability. The equations are solved using an adjoint-consistent Continuous Galerkin type discretization, specifically the Variational Multiscale with Discontinuous Subscales (VMSD) method. Furthermore, mesh adaptation is based on output error, with the output being the loudness perceived at ground. In particular, we consider the B-SEL metric, which requires the filtering of the ground pressure signal with the B-SEL transfer function. For this, we utilize a filter ODE approach in the time domain, which is well suited for our non-uniformly sampled ground signal, a consequence of the unstructured mesh adaptation. The output error is estimated employing the dual weighted residual method (DWR), with a correction accounting for the addition of artificial viscosity. We apply our framework to a practical case, with particular focus on the ground pressure signal and its resulting loudness metric. Our results show the advantage of adapting the mesh to the loudness metric rather than to an output based on the unfiltered pressure signal. Furthermore, we observe benefits of the higher-order method, as quadratic solutions converge the loudness metric faster than linear solutions.
April 11, 2025, CSE Community Seminar
Renato Trono Figueras
PhD Student,
Department of Aeronautics and Astronautics, MIT