Campus Units

Mechanical Engineering

Document Type


Publication Version

Accepted Manuscript

Publication Date


Journal or Book Title

Computers & Fluids



First Page


Last Page





We present a tetrahedral finite cell method for the simulation of incompressible flow around geometrically complex objects. The method immerses such objects into non-boundary-fitted meshes of tetrahedral finite elements and weakly enforces Dirichlet boundary conditions on the objects’ surfaces. Adaptively-refined quadrature rules faithfully capture the flow domain geometry in the discrete problem without modifying the non-boundary-fitted finite element mesh. A variational multiscale formulation provides accuracy and robustness in both laminar and turbulent flow conditions. We assess the accuracy of the method by analyzing the flow around an immersed sphere for a wide range of Reynolds numbers. We show that quantities of interest such as the drag coefficient, Strouhal number and pressure distribution over the sphere are in very good agreement with reference values obtained from standard boundary-fitted approaches. We place particular emphasis on studying the importance of the geometry resolution in intersected elements. Aligning with the immersogeometric concept, our results show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis. We demonstrate the potential of our proposed method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor.


This is a manuscript of an article published as Xu, Fei, Dominik Schillinger, David Kamensky, Vasco Varduhn, Chenglong Wang, and Ming-Chen Hsu. "The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometries." Computers & Fluids 141 (2016): 135-154. doi: 10.1016/j.compfluid.2015.08.027. Posted with permission.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Copyright Owner

Elsevier Ltd.



File Format


Published Version