This article reviews different types of forcing zones (sponge layers, damping zones, relaxation zones, etc.) as used in finite volume-based flow simulations to reduce undesired wave reflections at domain boundaries, with special focus on the case of strongly reflecting bodies subjected to long-crested incidence waves. Limitations and possible sources of errors are discussed. A novel forcing-zone arrangement is presented and validated via three-dimensional (3D) flow simulations. Furthermore, a recently published theory for predicting the forcing-zone behavior was investigated with regard to its relevance for practical 3D hydrodynamics problems. It was found that the theory can be used to optimally tune the case-dependent parameters of the forcing zones before running the simulations.
1. Introduction
Wave reflections at the boundaries of the computational domain can cause significant errors in flow simulations, and must therefore be reduced. In contrast to boundary element codes, where much progress in this respect has been made decades ago (see e.g., Clement 1996; Grilli &Horillo 1997), for finite volume-based flow solvers, there are many unresolved questions, especially:How to reliably reduce reflections and disturbances from the domain boundaries?How to predict the amount of undesired wave reflection before running the simulation?
This work aims to provide further insight to these questions for flow simulations based on Navier-Stokes-type equations (Reynolds-averaged Navier-Stokes, Euler equations, Large Eddy Simulations, etc.), when using forcing zones to reduce undesired reflections. The term "forcing zones" is used here to describe approaches that gradually force the solution in the vicinity of the boundary towards some reference solution, as described in Section 2; some examples are absorbing layers, sponge layers, damping zones, relaxation zones, or the Euler overlay method (Mayer et al. 1998; Park et al. 1999; Chen et al. 2006; Choi &Yoon 2009; Jacobsen et al. 2012; Kimet al. 2012; Schmitt & Elsaesser 2015; Perić & Abdel-Maksoud 2016a; Vukčević et al. 2016).
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