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

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 <6 × 10−5 after 2000 acoustic reflections) while NSCBC induced a global variation above 1% before code crashed.