A Tutorial on Non-Reflective Characteristic Boundary Conditions for Direct and Adjoint Time-Domain Acoustic Simulations
revision under review
- Accurate free-field acoustic simulations require non-reflective boundary conditions to suppress spu- rious reflections at the computational domain boundaries. Although several characteristic-based formulations for direct (forward) simulations have been proposed in recent decades, adjoint formu- lations of such characteristic-based boundary conditions (CBCs) have received limited attention in the literature and lack a comprehensive analysis. This paper presents the derivation and evaluation of adjoint CBCs complementing existing direct CBCs. Both direct and adjoint CBCs are applied to the nonlinear Euler equations and linear acoustic equations in time-domain simulations. The resulting boundary treatments are compared in terms of accuracy, reflection behavior, and direct-adjoint consistency. The CBCs are implemented using a single-point approach with both static and dynamic wave- vector estimates and are optionally combined with a sponge layer. Over the evaluated frequency range of 350 – 4000 Hz, spurious reflections are effectively attenuated in both direct and adjoint simulations. The adjoint CBCs show reflection behavior consistent with their direct counterparts, demonstrating that the proposed formulation provides a consistent open-boundary treatment for adjoint time-domain acoustics.
| 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: | 2026 |
| Notes: | under review |

