Campus Units

Mechanical Engineering

Document Type


Publication Version

Submitted Manuscript

Publication Date


Journal or Book Title

Computer Aided Geometric Design



First Page


Last Page





Computational fluid dynamics (CFD) simulations of flow over complex objects have been performed traditionally using fluid-domain meshes that conform to the shape of the object. However, creating shape conforming meshes for complicated geometries such as automobiles require extensive geometry preprocessing. This process is usually tedious and requires modifying the geometry, including specialized operations such as defeaturing and filling of small gaps.Hsu et al. (2016) developed a novel immersogeometric fluid-flow method that does not require the generation of a boundary-fitted mesh for the fluid domain. However, their method used the NURBS parameterization of the surfaces for generating the surface quadrature points to enforce the boundary conditions, which required the B-rep model to be converted completely to NURBS before analysis can be performed. This conversion usually leads to poorly parameterized NURBS surfaces and can lead to poorly trimmed or missing surface features. In addition, converting simple geometries such as cylinders to NURBS imposes a performance penalty since these geometries have to be dealt with as rational splines. As a result, the geometry has to be inspected again after conversion to ensure analysis compatibility and can increase the computational cost. In this work, we have extended the immersogeometric method to generate surface quadrature points directly using analytic surfaces. We have developed quadrature rules for all four kinds of analytic surfaces: planes, cones, spheres, and tori. We have also developed methods for performing adaptive quadrature on trimmed analytic surfaces. Since analytic surfaces have frequently been used for constructing solid models, this method is also faster to generate quadrature points on real-world geometries than using only NURBS surfaces. To assess the accuracy of the proposed method, we perform simulations of a benchmark problem of flow over a torpedo shape made of analytic surfaces and compare those to immersogeometric simulations of the same model with NURBS surfaces. We also compare the results of our immersogeometric method with those obtained using boundary-fitted CFD of a tessellated torpedo shape, and quantities of interest such as drag coefficient are in good agreement. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of a truck that has a large percentage of analytic surfaces. Using analytic surfaces over NURBS avoids unnecessary surface type conversion and significantly reduces model-preprocessing time, while providing the same accuracy for the aerodynamic quantities of interest.


This is a manuscript of an article published as Wang, Chenglong, Fei Xu, Ming-Chen Hsu, and Adarsh Krishnamurthy. "Rapid B-rep model preprocessing for immersogeometric analysis using analytic surfaces." Computer Aided Geometric Design 52 (2017): 190-204. DOI: 10.1016/j.cagd.2017.03.002. Posted with permission.

Copyright Owner

Elsevier B.V.



File Format


Published Version