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On the finite difference-based lattice Boltzmann method in curvilinear coordinates. (English) Zbl 0934.76074
The lattice Boltzmann method can be defined as a microscopic-based approach for solving the fluid flow problems at the macroscopic scales. The presently popular methods use regularly spaced lattices and cannot handle curved boundaries with desirable flexibility. To circumvent such difficulties, we present a finite difference-based lattice Boltzmann method (FDLBM) in curvilinear body-fitted coordinates on non-uniform grids. Several test cases, including the impulsively started cylindrical Couette flow, steady-state cylindrical Couette flow, steady flow over flat plates, and steady flow over a circular cylinder, are used to examine various issues related to the FDLBM. We also investigate the effect of boundary conditions for the distribution functions on the solution, the merits of second-order central difference and upwind schemes for advection terms, and the effect of the Reynolds number. \(\copyright\) Academic Press.

MSC:
76M28 Particle methods and lattice-gas methods
76M20 Finite difference methods applied to problems in fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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