ABSTRACT
For each lattice Boltzmann method, we computed solutions for two different initial conditions. Figure 1 and Figure 2 exhibit the solution at time t = 0 (the initial conditions) and timet = 1/32 for LB1 and LB2, respectively, for initial conditions satisfying the respective conditions of monotonicity. Figure 3 and Figure 4 exhibit the solution at time t = 0 (the initial conditions) and time t = 1/32 for LB 1 and LB2, respectively, for initial conditions not everywhere satisfying the respective conditions of monotonicity, e.g., the monotonicity conditions are not satisfied in either case at the locations (x, y) E(1/4, 1/4), (3/4, 1/4), (1/4, 3/4), (3/4, 3/4). At these points the initial occupation numbers exceed the respective conditions of monotonicity. The graphs at t = 1/32 are the result of the 256 X 256 finite difference computations.
