Lattice Boltzmann fractional advection scheme for achieving minimal numerical viscosity.

A new scheme with fractional particle advection is proposed for lattice Boltzmann models. This scheme recovers the same macroscopic hydrodynamics as the standard lattice Boltzmann method (LBM) under low-Mach numbers, weakly compressible and isothermal conditions. It achieves an effectively reduced Courant-Friedrichs-Lewy number so that the numerical stability is improved for simulation with a small viscosity. It overcomes the long-standing issue of increased numerical dissipation when the shear viscosity is dominant for fractional particle advection schemes and achieves accuracy of solution comparable to the standard LBM in any fractional situation. The new scheme also reveals that the origin of such increased numerical dissipation in fractional advection schemes lies in fractional advection of the nonequilibrium part of the particle distribution function. Overcoming the long-standing issue of excessive numerical dissipation when the shear viscosity is dominant due to fractional advection is a significant advancement in LBM, given the important advantages of fractional particle advection.