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To confine a spatial domain to a smaller computational domain, one needs artificial boundaries. This work considers the lattice Boltzmann method and deals with boundary conditions for these open boundaries. Ideally, such a condition does not interact with the fluid at all. We present novel two-dimensional discrete artificial boundary conditions to pursue that goal and we discuss four different versions. This type of condition is formulated on the discrete lattice Boltzmann level and does not require a PDE formulation of the fluid. We set a special focus on the D2Q9 model. Our numerical results compare the novel discrete artificial boundary conditions to simulations using the existing non-reflecting characteristic boundary condition and an exit boundary condition.

Discrete Artificial Boundary Conditions for the Lattice Boltzmann Method in 2D