A translating discontinuous-grid-block model for moving boundaries of finite thickness based on multi relaxation time version of LBM has been developed. In this regard, the execution of this model to simulate moving boundary flows has been demonstrated for the cases of a cylinder in simple shear flow, a single rigid wing executing 'clap and fling' motion, and the propulsion of a plunging flat plate. It is shown that the implementation of a body fitted refined mesh that moves along with the object improves its resolution and reduces the spurious oscillations registered in the force and velocity measurements compared to a single grid block. A number of interpolation schemes of linear, quadratic and cubic natures are assessed around the discontinuous grid interface. This method is highly suitable for problems that (a) involve large domain sizes in which the moving solid keeps traversing indefinitely in one direction, and (b) a high resolution around the body is demanded without the expenditure of additional computational power and memory as with the stationary discontinuous-grid-block.
NomenclatureA = plunging amplitude B = discrete velocity space c = lattice velocity C = chord length CD = drag coefficient CL = lift coefficient = kinetic energy f = velocity distribution function (SRT) FD = drag force per unit span FL = lift force per unit span x F = horizontal force on plunging plate G = shear rate H = height of channel = momentum flux K = moment space m = grid refinement ratio mp = mass of plate M = transformation matrix = viscous stress tensor q = energy density 2 Ref = flapping Reynolds number S = diagonal relaxation time matrix t = time T = duration of one cycle u = horizontal translational velocity U = dimensionless translational velocity Up = cylinder horizontal velocity Uw = wall velocity vmax = maximum plunging velocity V = maximum translational velocity Vp = cylinder vertical velocity xb = position vector of the boundary node xf = position vector of the fluid nodes at the interior of domain xs = position vector of solid node xp = horizontal position of flat plate y = instantaneous vertical displacement = dimensionless plunging amplitude f = moments of distribution function f = post collision distribution function (SRT) = post collision distribution function (MRT) = square of kinetic energy = flapping frequency = single relaxation time = kinematic viscosity c x = grid size in coarse block f x = grid size in fine block c t = time step in coarse block f t = time step in fine block = mass density ratio