Non-Reflecting Characteristic Boundary Conditions for Adjoint Time-Domain Acoustic Simulations
under review
- Accurate acoustic simulations in the free field require non-reflective boundary conditions to suppress spurious reflections at the computational domain boundaries. Although several characteristic-based formulations for direct (forward) simulations have been proposed in recent decades, the adjoint formulations of such characteristic-based boundary conditions (CBCs) have received limited atten- tion in the literature and lack a comprehensive analysis. This paper presents the derivation and evaluation of adjoint CBCs complementing the existing direct CBCs. Both the forward and adjoint CBCs are applied to the (nonlinear) Euler equations and linear acoustic equations in time-domain simulations. In this manner, the CBCs are investigated and subsequently compared to assess their respective accuracy and consistency. The CBCs were implemented using both a single-point and a zonal approach, with the former optionally combined with a sponge layer. Both approaches yielded comparable results in direct and adjoint simulations, while the zonal CBC exhibited improved ac- curacy at lower frequencies. Across the evaluated frequency range of approximately 350 – 5600 Hz, spurious reflections were attenuated by up to −70dB in both forward and adjoint cases, demon- strating the effectiveness and consistency of the proposed boundary treatment.
| Author: | Arne Hölter, Mathias Lemke, Stefan Weinzierl, Lewin SteinORCiD |
|---|---|
| Document Type: | Article |
| Parent Title (English): | Journal of Theoretical and Computational Acoustics |
| Year of first publication: | 2025 |
| Licence (German): | Creative Commons - CC BY - Namensnennung 4.0 International |


