Fluid Flow Topology Optimization Based On The Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is a newly developed numerical method for fluid simulation. The method, which is more general and flexible than other tra-ditional methods, is a mesoscopic-quantity-driven simulation approach. Owing to the development of computer techniques, especially the invention of parallel computation in recent years, the LBM has been widely applied in fast computations of large-scale fluid problems considering that it is naturally parallel. The optimization of fluid is an-other hot research field, and is used in the design of micro-fluidic devices, vehicles, ships and aircrafts. However, hardly have any efforts been made for the LBM based fluid optimization problems in the past.This research focuses on the fluid optimization problems solved by the LBM. The objective functionals (usually the energy dissipation), the design variables (which are defined by the density type optimization method), the control equation (i.e. the lattice Boltzmann equations (LBE)) and the other constraints like the volume limitation are selected to finally determine what the topology structures of the fluid channels would be like when the objectives go to the optima. In the optimization process, the original LBM is used to solve the forward problem (i.e. simulation), the adjoint sensitivity analysis is applied to LBM to get the adjoint lattice Boltzmann equations (ALBE), which is used to calculate the objective sensitivity with respect to the design variables. Through bringing the calculated objective and sensitivity into optimizing strategies, like the method of moving asymptotes (MMA), the topology of the channel structure can be optimized after iterative computations.In this research, the ALBE and the adjoint lattice Boltzmann method (ALBM), which are used to calculate the sensitivity, are derived through the adjoint sensitivity analysis. Based on this approach, a parallel computing program for solving the fluid topology optimization problems is developed on the Compute Unified Device Archi-tecture (CUDA). The appropriate optimization parameters are chosen according to a large amount of numerical tests. The new approach and the code are validated by nu-merical benchmarks, and the results are very similar to results achieved by traditional approaches. The new approach is then used to design bifurcating channels, a simple fluidic device.This research based on LBM is an extension to the current optimization theory. The new theory is proved to be highly numerically similar with the other optimization theories, meanwhile it is more general, more parallel and more stable, and is an ef-fective theory to solve the fluid optimization problems based on the highly developed modern computing facilities. In this research, the acceleration technique is used to pur-sue high performances where both forward and adjoint problems are implemented on the Graphic Processing Unit (GPU).