ABSTRACT
Accurate and efficient numerical simulation of fluid flow around complex and moving geometries remains a central challenge in computational fluid dynamics. Traditional domain-fitted mesh approaches require the computational mesh to conform to geometric boundaries, often leading to mesh distortion, costly remeshing, and limited robustness for intricate shapes, thin boundary layers, or large motions. Embedded mesh methods offer an attractive alternative by embedding complex physical domains into simple background meshes, simplifying mesh generation and improving automation and scalability. However, the predominant use of Cartesian background meshes yields uniform spatial accuracy and insufficient resolution in high-error regions, such as boundary layers and strong flow gradients, especially at high Reynolds numbers.
This thesis addresses these limitations by developing scalable hybrid strategies that couple embedded formulations with adaptive mesh techniques. Two complementary approaches are employed: the r-method, which improves accuracy through continuous mesh deformation without changing mesh topology, and the h-method, which locally refines or coarsens the mesh based on error indicators. The r-method is first coupled with the embedded finite element method to form the r-EFEM, enabling anisotropic, high-aspect-ratio elements aligned with boundary layers while preserving computational efficiency and parallel scalability. A robust linearization strategy is introduced to efficiently solve the nonlinear mesh optimization problem.
To capture localized flow features away from boundary layers, the r-EFEM is further combined with a hierarchical h-refinement strategy with hanging nodes, leading to the proposed r–h EFEM. This hybrid formulation integrates anisotropic boundary-layer resolution via mesh deformation, localized refinement in high-error regions, and geometry-independent discretization within the embedded framework. Hanging-node contributions are incorporated directly into the finite element formulation to preserve conformity and numerical stability, while an error estimator guides adaptive refinement and mesh redistribution.
The methods are validated using benchmark problems involving fixed and moving geometries, including high-Reynolds-number flows with thin boundary layers and complex vortex dynamics. The results demonstrate substantial accuracy improvements over standard embedded approaches while maintaining robustness and computational efficiency. In moving-domain simulations, the hybrid framework eliminates remeshing and prevents mesh degradation, enabling stable and scalable transient simulations. This work establishes a unified adaptive framework for accurate embedded finite element simulations in complex and evolving geometries.
PhD Advisors:
CANDIDATE
Saman Rahmani is a researcher and simulation engineer specialized in computational fluid dynamics (CFD) and advanced numerical methods. His work focuses on r–h adaptive embedded finite element methods (FEM) for high-Reynolds-number incompressible flows, moving boundaries, and complex geometries. He has worked with finite volume and finite difference methods (FVM/FDM) for compressible flows, aeroacoustics, and shock–turbulence interaction and has experience in the full simulation workflow — from pre-processing, CAD-based mesh generation, and .stl geometry handling to solver development and post-processing. Skilled in solving nonlinear systems, mesh adaptation, and high-performance computing using C++ and Python, Rahmani bridges advanced numerical modelling with real-world aerodynamic applications.