An explicit conservative finite volume scheme based on multi-scale characteristic lines is proposed for the simulation of advection and convection in fluid flows. By representation of the Navier–Stokes equation in a kinetic manner, the evolution of particle distribution functions on discrete velocity space is governed by the kinetic advection equation. The control equation is discretized and integrated along particle velocity characteristic lines via a temporal/spatial related reconstruction to obtain accurate macroscopic fluxes. With a D2Q37 lattice velocity model, the collision processes are modeled by a relaxation term expressed with Hermite expansion to reduce complexity and computational cost. Several cases, including the Sod shock tube case, lid-driven cavity flows, and natural convection flows on Rayleigh numbers of 103–106, Rayleigh–Bénard convection flows on Rayleigh numbers of 104–106 and Rayleigh–Taylor instability on the Reynolds number of Re = 62 990 are simulated and analyzed. Simulation results show satisfactory accuracy with a relative L2-norm error less than 1% as compared with benchmark data, and reveal several steady and unsteady mechanisms, including advection in the Riemann problem, buoyancy-driven motion, temperature-driven mass transfer, interface dynamical behaviors, and vortex evolution in convective flows.
Pan et al. (Sun,) studied this question.
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