Multiphase flow problems are ubiquitous in many engineering disciplines like in chemical and process engineering, where the interaction of different phases such as liquids or gases strongly influences system performance. Accurate modeling of multiphase flow phenomena therefore is a crucial cornerstone for optimizing system design and control. A widely recognized modeling approach is the combi-nation of the Navier-Stokes equations–the fundamental governing equations of fluid dynamics–with phase-field approaches like the Cahn-Hilliard model, allowing to capture fluid mixtures of different densities or viscosities. The solution of the resulting set of coupled equations requires numerical approximation techniques such as the finite element method, and ideally robust solvers that effectively han-dle the resulting linearized discrete equation systems. While direct solvers are most promising for small- to medium-sized applications, large scale scenarios require iterative solution strategies on high-performance computing machines for optimal performance and feasibility. However, these approaches need robust pre-conditioning strategies in order to converge and be effective.
In this thesis, preconditioners suitable for the coupled monolithic set of Cahn-Hilliard Navier-Stokes equations should be investigated, implemented, tested, and compared across different examples, and an optimal strategy should be devised.
Description of Task:
- Literature review on (block) preconditioning strategies for the monolithic Cahn-Hilliard-Navier-Stokes system
- Review of Schur complement preconditioners for the Navier-Stokes equa-tions, with focus on approximation methods for the Schur complement
- Implementation of preconditioners into an existing (FEniCSx-based) Cahn-Hilliard-Navier-Stokes solver in a Python environment interfacing with the linear algebra suite PETSc
- Derivation of (2D and 3D) benchmark examples and investigation of weak and strong scaling of the solvers
- Investigation of solver hyperparameters for optimal convergence
Desirable Knowledge and Skills:
- Familiarity with computational fluid dynamics, ideally two-phase flow
- Conceptual understanding of the finite element method
- Basic knowledge of linear solvers and preconditioners
- Programming experience, ideally Python
In division 2.2, research focuses on the development of dynamic process models to describe all system states from start-up to shutdown, supported by an open library of dynamic, pressure-driven models. The division uses machine learning, uncertainty quantification and hybrid modeling methods to drive forward real-time application and plant monitoring. For the comprehensive digitalization of process engineering, the division is also researching information and data modelling as well as process models from engineering to the operation of chemical plants. This is supplemented by the development of methods for the safe and optimal transformation of chemical plants.
Start: immediately
Contact person:
Dr.-Ing. Marc Hirschvogel
marc.hirschvogel@bam.de
Leonardo Frazao
leonardo.lorena.palito.frazao@tu-berlin.de