Extended volumetric scheme for lattice Boltzmann models.

: An extended volumetric scheme is proposed for lattice Boltzmann (LB) models. This scheme is particularly desirable for multispeed LB models due to its removal of nonlocal advection. It recovers the same macroscopic hydrodynamics as the standard lattice Boltzmann method without any further treatments. This scheme achieves an effectively reduced Courant-Friedrichs-Lewy number so that numerical stability is significantly enhanced for high Reynolds number simulations while maintaining the same order of numerical accuracy.