Abstract
The coupling of two-dimensional (2D) and one-dimensional (1D) models to form a single hybrid 2D–1D model is considered, for the time-dependent linear wave equation. The 1D model is used to represent a 2D computational domain where the solution behaves approximately in a 1D way. This hybrid model, if designed properly, is a more efficient way to solve the full 2D model for the entire problem. The paper focuses on the way the 2D–1D coupling is done, and on the coupling error generated. The Nitsche method is used for the mixed-dimensional coupling, thus extending previous work, which considered steady-state problems, to the time-dependent case. The hybrid formulation is derived, and the numerical accuracy and efficiency of the method is explored using numerical examples. The performance of this coupling method is compared to that of the simpler Panasenko method. It is shown that in some cases the former is more tolerant to a poor choice for the location of the 2D–1D interface.
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