Advanced Lattice Boltzmann Models for the Simulation of Additive Manufacturing Processes

This thesis presents the three–dimensional modeling, discretization, implementation, and simulation of additive manufacturing processes on the example of electron beam melting (EBM). The fluid dynamics of the liquified melting pool are modeled by the incompressible Navier–Stokes equations and the incorporation of energy by the heat equation. The applied numerical scheme is a thermal multi–distribution lattice Boltzmann method (LBM) allowing an efficient parallel implementation. The liquid phase of the melting pool and the gas phase of the atmosphere are separated by the free surface lattice Boltzmann method (FSLBM) that does not compute the dynamics of the gas phase explicitly but sets a boundary condition at the interface. Furthermore, the electron beam gun and the metal powder particles are explicitly modeled. A realistic particle size distribution is achieved by using an inverse Gaussian distribution. For the absorption of energy two different algorithms are derived depending on the acceleration voltage of the electron beam. Most of the EBM specific algorithms are embedded in the highly parallel lattice Boltzmann framework WALBERLA. The metal powder particles are simulated by the also highly parallel physics engine pe. Within the coupling particles are represented as rigid bodies in the pe and treated as boundaries in the LBM scheme of WALBERLA. Both frameworks work on state–of–the–art supercomputers. The EBM application and its implementation are validated by benchmarks where analytical solutions are common knowledge. Moreover, the simulation results are compared to experimental data with respect to quality of the product in order to avoid porosity, and ensure dimensional accuracy. Since the numerical and experimental data are highly concordant the implemented EBM model is suitable to develop new processing strategies in order to improve the quality of the products. The simulations support machine users and developers in order to find an optimal parameter set for specific parts. Lastly, the accuracy order of the applied free surface boundary condition is examined via the Chapman–Enskog expansion since it has a huge influence on the simulation results. It is established that the original FSLBM boundary condition is just first order accurate for general cases and since the LBM is second order accurate the overall accuracy is reduced by applying FSLBM. In order to overcome this deficiency an improved second order FSLBM boundary condition is derived successfully. The importance and correctness of this new FSLBM boundary condition is finally underlined by a thorough validation against analytical calculations and experiments.