In this study, the lattice Boltzmann method (LBM), based on the underlying statistical mechanics on assumed fluid particle population interacting over a discrete lattice mesh, is used to simulate fluid flows. LBM solves the macroscopic properties density, velocity and pressure of fluid modeled by the Navier-Stokes equations. Assuming a desired fluid behavior, we define an optimal control problem that has an objective function indicating the proximity of a simulated fluid behavior to the desired fluid behavior, and has the incompressible Navier-Stokes equations as the constraint. We aim to find the optimal control, in the form of an external volume force on fluid, that steers the fluid simulation towards the desired behavior. We perform the discrete adjoint method, a technique to determine the gradient of the objective function efficiently, that utilizes the LBM as a discrete solver of the constraint incompressible Navier-Stokes equations of the optimal control problem. Finally, we apply the method of steepest descent, an iterative method that uses the computed gradient, to search for the control that drives the simulation to optimality.

Optimal Control of Fluids based on Lattice Boltzmann Method Discretizations

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Optimal Control of Fluids based on Lattice Boltzmann Method Discretizations