Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Mechanical Engineering


Mechanical Engineering

First Advisor

Ming-Chen Hsu


This dissertation presents the development of a novel immersogeometric method for the simulation of turbulent compressible flows around complex geometries.

The immersogeometric analysis is first extended into the version of tetrahedral finite cell method, in order to handle complex geometries flexibly and accurately. The developed method immerses complex objects into non-boundary-fitted meshes of tetrahedral finite elements which can be easily refined in interesting regions. Adaptively-refined quadrature rules faithfully capture the flow do- main geometry in the discrete problem without modifying the non-boundary-fitted finite element mesh. Particular emphasis is placed on studying the importance of the geometry resolution in in- tersected elements. Aligning with the immersogeometric concept, the results show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis.

To simulate the compressible flows in an accurate and and robust way, a novel stabilized finite element formulation is developed. New weak imposition of essential boundary conditions and sliding-interface formulations are also proposed in the context of moving-domain compressible flows. The new formulation is successfully tested on a set of examples spanning a wide range of Reynolds and Mach numbers showing its superior robustness. Experimental validation of the new formulation is also carried out with good success.

The developments of tetrahedral finite cell method and the stabilized finite element formulations are combined to further develop the immersogeometric method for compressible flows. Non-symmetric Nitsche method is used in the weak-boundary-condition operator, to offer good performance in the context of non-boundary-fitted discretization. The developed immersogeomet- ric method is tested against several benchmark problems, to prove its comparable accuracy to its boundary-fitted counterpart. Finally, the aerodynamic analysis of a UH-60 helicopter is carried outusing the developed method, to illustrate its potential to support design of real engineering systems through high-fidelity aerodynamic analysis.


Copyright Owner

Fei Xu



File Format


File Size

139 pages

Included in

Engineering Commons