Open Access

Patrick Zimbrod

• The accurate representation and prediction of physical phenomena through numerical computer codes remains a vast and intricate interdisciplinary topic of research. Especially within the last decades, there has been a considerable push toward high-performance numerical schemes to solve partial differential equations (PDEs) from the applied mathematics and numerics community. The resulting landscape of choices regarding numerical schemes for a given system of PDEs can thus easily appear daunting for an application expert who is familiar with the relevant physics, but not necessarily with the numerics. These high-performance schemes in particular pose a substantial hurdle for domain scientists regarding their theory and implementation. In this thesis, a unifying scheme for grid-based approximation methods is proposed to address this issue. Some well-defined restrictions are introduced to systematically guide an application expert through the process of classifying a given multiphysicsThe accurate representation and prediction of physical phenomena through numerical computer codes remains a vast and intricate interdisciplinary topic of research. Especially within the last decades, there has been a considerable push toward high-performance numerical schemes to solve partial differential equations (PDEs) from the applied mathematics and numerics community. The resulting landscape of choices regarding numerical schemes for a given system of PDEs can thus easily appear daunting for an application expert who is familiar with the relevant physics, but not necessarily with the numerics. These high-performance schemes in particular pose a substantial hurdle for domain scientists regarding their theory and implementation. In this thesis, a unifying scheme for grid-based approximation methods is proposed to address this issue. Some well-defined restrictions are introduced to systematically guide an application expert through the process of classifying a given multiphysics problem, identifying suitable numerical schemes and implementing them. By defining a fixed set of input parameters, amongst them for example the governing equations and the hardware configuration, the process can be executed in a systematic and reproducible manner. This method not only helps to identify and assemble suitable schemes but enables the unique combination of multiple methods. This process and its effectiveness are exemplarily demonstrated using different approaches. As a practically relevant and complex multiphysics problem, the powder bed scale process dynamics during Laser Powder Bed Fusion is investigated. After a thorough investigation of current simulation approaches, it is shown how this work contributes to enhancing the current state of research by proposing a tailored discretization to this problem. Overall, it is systematically shown how one can exploit some given properties of a PDE problem to attain an efficient compound discretization.…