Applicant
Prof. Dr. Wolfgang A. Wall
Institute for Computational Mechanics
Technical University of Munich (TUM)
Project Overview
High-fidelity computational fluid dynamics (CFD) simulations have become an essential tool for analyzing complex engineering systems, ranging from aerodynamic applications to strongly coupled multiphysics problems such as fluid-structure interaction. Achieving predictive simulations for realistic geometries requires highly efficient numerical methods and scalable algorithms capable of exploiting modern high-performance computing (HPC) systems. Over the last decade, matrix-free finite element methods have emerged as one of the most successful approaches for large-scale CFD simulations, enabling excellent performance and scalability on modern supercomputers. However, many existing high-performance implementations are optimized for structured hexahedral meshes, while practical engineering applications frequently rely on tetrahedral or hybrid meshes to accurately represent complex geometries and boundary layers.
While tetrahedral meshes are significantly easier to generate for geometrically complex domains, they generally offer lower computational efficiency because they cannot fully exploit tensor-product structures and sum-factorization techniques. Mixed-element discretizations provide a promising compromise: tetrahedral elements are used near intricate boundaries, while computationally efficient hexahedra constitute most of the interior domain, with pyramids and wedges providing conforming transitions between the different element types.
The goal of this project is to extend the high-performance CFD solver ExaDG (github.com/exadg), which is based on deal.II (dealii.org), to operate efficiently on heterogeneous meshes. This includes the development of suitable preconditioning and solver strategies that account for different element types within the same computational domain. To support scalable mesh management and adaptive refinement, the mesh library t8code (dlr-amr.github.io/t8code) will be integrated as a backend into deal.II. The project aims to make advanced CFD algorithms accessible within realistic industrial meshing workflows while preserving the excellent scalability already demonstrated on large HPC systems.
Furthermore, the project will advance the integration of these libraries with the multiphysics framework 4C (4c-multiphysics.org), targeting monolithic fluid-structure interaction simulations. Efficient coupling techniques for non-matching interface meshes will be developed, enabling independent discretizations and refinement strategies in the fluid and structural subdomains while maintaining scalable performance on distributed-memory HPC systems.
Overall, the project aims to establish a complete HPC-ready simulation stack for multiphysics CFD applications on mixed-element meshes. By combining scalable mesh management, high-performance matrix-free solvers, and advanced multiphysics capabilities, the resulting framework will significantly broaden the range of realistic applications that can benefit from next-generation high-performance computing technologies.