No-slip wall acoustic boundary condition treatment in the incompressible limit

• Published in: Computers & fluids 2013-11, Vol.86, p.92-102
• Main Authors: Cuif Sjöstrand, Marianne, D’Angelo, Yves, Albin, Eric
• Format: Article
• Language: English
• Subjects: Acoustics; Boundary conditions; Characteristic boundary conditions; Computational fluid dynamics; Direct numerical simulation; Fluid flow; Fluid mechanics; Incompressible limit; Mathematical models; Mechanics; No-slip wall; Physics; Reflection; Strategy; Walls
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2013.07.015

•We wish to implement a stable acoustic BC treatment for no-slip walls.•We extend the 3DNSCBC approach for a high accuracy FD solver.•The incompressible limit of 3D Euler equations is fulfilled.•Some validation tests are proposed, in particular a pressure wave train in a 2D channel. A characteristic formulation for the numerical treatment of acoustically reflecting no-slip wall boundary condition is presented and numerically validated for some discriminating situations. As an extension of the 3DNSCBC popular approach, this NSWIL strategy relaxes smoothly towards a 3DNSCBC strategy for a slipping wall – the Euler equations natural wall boundary condition – when the viscosity goes to zero. Using our in-house 6th order FD solver, some comparative tests were performed. In particular, we computed a pressure wave train in a 2D periodic channel, leading to standing acoustic waves. Long time runs using NSWIL strategy and involving 2.5×105 temporal iterations and 2×103 acoustic reflections at the walls show no numerical instability while popular NSCBC strategy turns out to be unstable after less than 100 reflections. In that case, global mass conservation was very precisely ensured using NSWIL (relative loss