Improving the accuracy of lattice Boltzmann simulations of liquid microflows

The simulation of incompressible flows at very low Reynolds numbers (Stokes regime) with the standard lattice Boltzmann method (collision-propagation algorithm) is hindered by a limitation of accuracy due to the relationship between viscosity and the Mach and Reynolds numbers.We present a multirelaxation-time lattice-Boltzmann method with modified equilibrium moments that allows improvement of accuracy for a given resolution at very low-Reynolds-number flows. This is paramount for liquid microflow simulations and for multiscale coupling in many practical instances, such as when the fluid motion is highly influenced by bounding or particulate immersed solids. The method as presented is restricted to steady-state flows, which include many fluid-flow applications at the microscale. The viscous flow with slip of a liquid in a long microchannel, for which an analytical solution exists, has been used as the test case.