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A new treatment of no slip boundary condition on complex geometry in a lattice Boltzmann method is proposed. We developed Space-Time Bounce-Back (STBB) method, which evaluate distribution functions in the vicinity of the solid boundary whose geometry described in the scale less than the lattice size. The STBB method is based on not only the spatial distribution but also the temporal distribution of distribution functions, in order to satisfy both the complete reflection on the solid boundary and the second order accuracy in the spatial discretization. Two-dimensional channel flow is calculated by using the proposed method, and both the accuracy and the stability are examined by comparing with the analytical solution.

No-slip Boundary Condition on Complex Geometry in Lattice Boltzmann Method (1st Report, Construction of Space-Time Bounce-Back Method)