Rapid B-rep model preprocessing for immersogeometric analysis using analytic surfaces

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 like 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 toroids. 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.

[1]  Zhi J. Wang,et al.  An adaptive Cartesian grid generation method for ‘Dirty’ geometry , 2002 .

[2]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[3]  Yuri Bazilevs,et al.  An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. , 2015, Computer methods in applied mechanics and engineering.

[4]  Ming-Chen Hsu,et al.  The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometries , 2016 .

[5]  T. Hughes,et al.  Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes , 2010 .

[6]  J. Nitsche Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind , 1971 .

[7]  Firoz Alam,et al.  A study on aerodynamic drag of a semi-trailer truck , 2013 .

[8]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[9]  Joe Walsh,et al.  A comparison of techniques for geometry access related to mesh generation , 2004, Engineering with Computers.

[10]  Iddo Hanniel,et al.  Direct Rendering of Solid CAD Models on the GPU , 2011, 2011 12th International Conference on Computer-Aided Design and Computer Graphics.

[11]  Paresh Parikh,et al.  Generation of three-dimensional unstructured grids by the advancing-front method , 1988 .

[12]  Gershon Elber,et al.  Performing Efficient NURBS Modeling Operations on the GPU , 2009, IEEE Trans. Vis. Comput. Graph..

[13]  Thomas J. R. Hughes,et al.  Weak imposition of Dirichlet boundary conditions in fluid mechanics , 2007 .

[14]  Ernst Rank,et al.  The finite cell method for three-dimensional problems of solid mechanics , 2008 .

[15]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[16]  Yuri Bazilevs,et al.  Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models , 2015, Computational mechanics.

[17]  Adarsh Krishnamurthy,et al.  Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces , 2009, Comput. Aided Des..

[18]  Thomas J. R. Hughes,et al.  Fluid–structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation , 2014, Computational Mechanics.

[19]  T. Hughes,et al.  Large Eddy Simulation and the variational multiscale method , 2000 .

[20]  Ming-Chen Hsu,et al.  The tetrahedral finite cell method: Higher‐order immersogeometric analysis on adaptive non‐boundary‐fitted meshes , 2016 .

[21]  Robert J. Englar,et al.  Advanced Aerodynamic Devices to Improve the Performance, Economics, Handling and Safety of Heavy Vehicles , 2001 .

[22]  Adarsh Krishnamurthy,et al.  Direct immersogeometric fluid flow analysis using B-rep CAD models , 2016, Comput. Aided Geom. Des..

[23]  David L. Marcum,et al.  Unstructured Grid Generation for Aerospace Applications , 2000 .

[24]  Hamid Ghazialam,et al.  Surface mesh generation for dirty geometries by the Cartesian shrink-wrapping technique , 2010, Engineering with Computers.

[25]  Marco S. Pigazzini,et al.  Optimizing fluid–structure interaction systems with immersogeometric analysis and surrogate modeling: Application to a hydraulic arresting gear , 2017 .

[26]  Commercial vehicles , 2012 .

[27]  Victor M. Calo,et al.  Weak Dirichlet Boundary Conditions for Wall-Bounded Turbulent Flows , 2007 .