arXiv subjects

Patrick Zimbrod

Publications and source records attributed to Patrick Zimbrod.

4 recordsLinked to original sources

arXiv2023

An Application Driven Method for Assembling Numerical Schemes for the Solution of Complex Multiphysics Problems

Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely remains the status quo for scientists and engineers focusing on applying simulation tools to specific problems in practice. We attribute this growing technical gap to the increasing complexity and knowledge required to pick and assemble state-of-the-art methods. Thus, with this work, we initiate an effort to build a common taxonomy for the most popular grid-based approximation schemes to draw comparisons regarding accuracy and computational efficiency. We then build upon this foundation and introduce a method to systematically guide an application expert through classifying a given PDE problem setting and identifying a suitable numerical scheme. Great care is taken to ensure that making a choice this way is unambiguous, i.e. the goal is to obtain a clear and reproducible recommendation. Our method not only helps to identify and assemble suitable schemes but enables the unique combination of multiple methods on a per-field basis. We demonstrate this process and its effectiveness using different model problems, each comparing the resulting numerical scheme from our method with the next best choice. For both the Allen Cahn and advection equations, we show that substantial computational gains can be attained for the recommended numerical methods regarding accuracy and efficiency. Lastly, we outline how one can systematically analyze and classify a coupled multiphysics problem of considerable complexity with 6 different unknown quantities, yielding an efficient, mixed discretization that in configuration compares well to high-performance implementations from the literature.

math.NA↗

arXiv2022

Efficient Simulation of Complex Capillary Effects in Advanced Manufacturing Processes using the Finite Volume Method

The accurate representation of surface tension driven flows in multiphase systems is considered a challenging problem to resolve numerically. Although there have been extensive works in the past that have presented approaches to resolve these so called Marangoni flows at the phase boundaries, the question of how to efficiently resolve the interface in a universal and conservative manner remains largely open in comparison. Such problems are of high practical relevance in many manufacturing processes, especially in the microfluidic regime where capillary effects dominate the local force equilibria. In this work, we present a freely available numerical solver based on the Finite Volume Method that is able to resolve arbitrarily complex, incompressible multiphase systems with the mentioned physics at phase boundaries. An efficient solution with respect to the number of degrees of freedom can be obtained by either using high order WENO stencils or by employing adaptive cell refinement. We demonstrate the capabilities of the solver by investigating a model benchmark case as well as a single track laser melting process that is highly relevant within laser additive manufacturing.

math.NA↗

arXiv2021

Modelling of microstructures during in-situ alloying in additive manufacturing for efficient material qualification processes

In this work, a numerical simulation framework is presented based on the Phase Field Method that is able to capture the evolution of heterogeneous metallic microstructures during solidification. The involved physics can prove especially useful when studying not only systems undergoing thermal gradients, such as in homogeneous systems, but also in conditions that exhibit stark spatial gradients, i.e. when these inhomogeneities are present even on a mesoscopic scale. To illustrate the capabilities of the model, in-situ alloying of a High Entropy Alloy during Laser Powder Bed Fusion is investigated as an exemplary use case. The resulting digital twin is expected to shorten development times of new materials as well as cut down on experimental resource needs considerably, therefore contributing to efficient material qualification processes.

cond-mat.mtrl-sci↗

arXiv2019

Frictionless motion of diffuse interfaces by sharp phase-field modeling

Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution. However, the numerical representation of moving diffuse interfaces on discrete numerical grids involves spurious grid friction, which limits the overall performance of the model in many respects. Interestingly, this intricate and detrimental effect can be overcome in Finite Difference (FD) and Fast Fourier Transformation (FFT) based implementations by employing the so-called Sharp Phase-Field Method (SPFM). The key idea is to restore the discretization induced broken Translational Invariance (TI) in the discrete phase-field equation by using analytic properties of the equilibrium interface profile. We proof that this method can indeed eliminate spurious grid friction in the three dimensional space. Focussing on homogeneous driving forces, we quantitatively evaluate the impact of spurious grid friction on the overall operational performance of different phase-field models. We show that the SPFM provides superior degrees of interface isotropy with respect to energy and kinetics. The latter property enables the frictionless motion of arbitrarily oriented diffuse interfaces on a fixed 3D grid.

cond-mat.mtrl-sci↗