Analysis of the accuracy and pressure oscillation of the lattice Boltzmann method for fluid-solid interactions

Investigations have been conducted to analyze the accuracy of the ghost fluid immersed boundary lattice Boltzmann method and the conventional interpolation/extrapolation bounce-back schemes. The intrinsic sources of pressure oscillation for numerical simulation of moving boundary flows have also been investigated. An existing bilinear ghost fluid immersed boundary lattice Boltzmann method (BGFM) (Tiwari and Vanka, 2012) and a proposed quadratic ghost fluid immersed boundary lattice Boltzmann method (QGFM) have been compared with Guo's second-order extrapolation bounce-back scheme (Guo et al.) and the linear and quadratic interpolation bounce-back scheme (LIBB, QIBB) (Bouzidi et al., 2001; Lallemand and Luo, 2003). To study the numerical pressure oscillations in the moving boundary problem, (i) three existing refilling techniques and one proposed refilling technique are compared; (ii) three collision models, including the single-relaxation-time model, the multiple-relaxation-time model and the two-relaxation-time model, are investigated; (iii) two force evaluation schemes, a Galilean invariant momentum exchange method Wen et al. and a stress integration method Inamuro et al., are considered. The accuracy and the performance in pressure oscillation suppression for the studied numerical approaches are compared and discussed by five numerical examples: an eccentric cylinder flow, a Cylindrical Couette flow, an impulsively started cylinder in a channel, an oscillation cylinder in calm water and a particle suspension problem. The numerical results indicate that the accuracy of QGFM scheme is comparable to Guo's scheme while the accuracy of BGFM is worse than both of them. The QIBB scheme shows the best performance in the space convergence accuracy among all the schemes. Selection of the collision model, refilling technique and force evaluation scheme affect the pressure oscillation phenomenon in moving boundary simulations remarkably.