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Convergence of lattice Boltzmann methods for Navier-Stokes flows in periodic and bounded domains. (English) Zbl 1160.76038
Summary: Combining an asymptotic analysis of the lattice Boltzmann method with a stability estimate, we are able to prove some convergence results which establish a strict relation to incompressible Navier-Stokes equations. The proof applies to the lattice Boltzmann method in the case of periodic domains and for specific bounded domains if the Dirichlet boundary condition is realized with the bounce back rule.

MSC:
76M28 Particle methods and lattice-gas methods
76D05 Navier-Stokes equations for incompressible viscous fluids
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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