COUPLED 2023

Mixed-Dimensional Coupling using the DtN Method for Time-Dependent Acoustics

  • Givoli, Dan (Technion - Israel Institute of Technology)
  • Rabinovich, Daniel (Technion - Israel Institute of Technology)

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We consider the coupling of a 2D model and a 1D model, to form a hybrid mixed-dimensional model, in the context of acoustic wave propagation. A Dirichlet-to-Neumann (DtN) method is used to perform this coupling in the time domain. It is based on enforcing the continuity of the DtN map, relating the unknown function (acoustic pressure) to its spatial derivatives, on the 2D-1D interface. This is an extension to the time domain of a previous DtN coupling method used for steady-state problems [1]. The governing equations are discretized in space using the Finite Element Method (FEM), introducing a convolution term in time in the semi-discrete equations due to the DtN coupling. The resulting set of integro-differential equations is solved in time using an extension of the Newmark explicit method [2], with the corresponding treatment of the convolution term. We study the performance of the proposed coupling method in a waveguide setting, and give an illustrative example of acoustic waves in a horn, that utilizes this procedure. We conclude that the present method is a viable tool for mixed-dimensional coupling. REFERENCES [1] Ofir, Y. and Givoli, D. DtN-based mixed-dimensional coupling using a Boundary Stress Recovery technique, Comput. Methods Appl. Mech. Engrg. (2015), 287:31{53. [2] Patlashenko, I., Givoli, D. and Barbone, P. Time-stepping schemes for systems of Volterra integro-differential equations. Comput. Methods. Appl. Mech. Engng. (2001) 190:5691{5718