Introducing a variable speed of sound in single-component lattice Boltzmann simulations of isothermal fluid flows

To simulate the hydrodynamics and mixing characteristics of chemical reactors by means of a lattice Boltzmann method (LBM), it is essential to consider components with varying molecular weights (and therefore speeds of sound). This option requires modification of the standard equilibrium distribution function and the use of an extended velocity set. In this paper, we show that, for isothermal incompressible single-component non-reactive flows, tuning the speed of sound with a modified equilibrium distribution and an extended velocity set allows for reproducing the proper flow characteristics with strongly reduced errors (compared to LBM simulations on standard lattices). This is done for two isothermal benchmarks, viz. a damped standing pressure wave and a decaying viscous Taylor-Green Vortex. The convergence as a function of the number of lattice nodes used improves substantially for varying values of the speed of sound.