March 01, 2010
CFD: Of Meshes and Math
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Jeff Rowe - Managing Editor

by Jeff Rowe - Contributing Editor
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As Mr. Bruegel points out, the fundamental basis of most CFD problems are the Navier-Stokes equations that define fluid flow through approximation. These equations can be simplified by removing terms describing viscosity to yield Euler equations. Further simplification, by removing terms describing vortices produces full potential equations, and these equations can be linearized to yield linearized potential equations.

Historically, the first CFD methods were developed to solve linearized potential equations. Two-dimensional methods, using conformal transformations of the flow about a cylinder or the flow around an airfoil were developed in the 1930s. As computer power became more available three-dimensional CFD methods were developed.

The fundamental consideration in CFD is treating a continuous fluid using a discrete method. One method is to divide a space (spatial domain) into smaller volume spaces to form a volume mesh or grid, and then apply a suitable algorithm to solve the equations of motion (Euler equations for non-viscous, and Navier-Stokes equations for viscous flow).

Although usually complex, it is possible to directly solve Navier-Stokes equations for laminar flows and turbulent flows when they can be resolved by a grid. Generally, however, the range appropriate to the problem is larger than even today's massively parallel computers can handle. In these cases, turbulent flow simulations require turbulence models, such as large eddy simulations (LES) and the Reynolds-averaged Navier-Stokes (RANS) equations.

For really complex problems, other equations are solved simultaneously with the Navier-Stokes equations. These other equations can include those describing concentration (mass transfer), chemical reactions, heat transfer, etc. More advanced algorithms can simulate more complex fluid problems involving multi-phase flows (such as liquid/gas, solid/gas, liquid/solid), non-Newtonian fluids (such as blood), or chemically reactive flows (such as combustion).

Regardless of the approach, the same basic procedure is followed for solving CFD problems:
  • A preprocessor defines the geometry (physical bounds) of the problem, the volume occupied by the fluid is divided into a uniform or non uniform. mesh, the boundary conditions and physical modeling are defined

  • The simulation is started and the equations are solved.

  • A postprocessor analyzes and visualizes the result.
  • Obviously, what goes on behind the scenes is a lot more complicated than that, but those are the basic steps that are followed.

    So, will CFD be the next “big thing” in the simulation/analysis arena that makes the grade in MCAD products? Tomorrow? Maybe not. Going forward? I'd say the odds are pretty good that that's a pretty safe bet as all types of simulation and analysis move forward in the design process.

    The Week's Top 5

    At MCADCafé we track many things, including the stories that have attracted the most interest from our subscribers. Below are the five news items that were the most viewed during last week.

    Dassault Systèmes (DS) launched Release 20 of its collaborative V5 PLM portfolio, including CATIA, ENOVIA, SIMULIA, and DELMIA. The launch of V5R20 includes enhancements to DS' ENOVIA SmarTeam multi-CAD collaboration software, integration of SIMULIA's nonlinear and thermal realistic simulation capabilities into the V5 platform, as well as composites design and simulation capabilities in the CATIA and SIMULIA portfolios. V5R20 also features enhancements across the entire product portfolio, including digital manufacturing. V5's openness is advanced in Release 20 with updated multi-CAD integrations and a new 3D viewer available directly within ENOVIA SmarTeam. In addition, V5R20
    introduces a new product, CATIA Extended STEP Interface. It enhances large assembly archiving with nested assembly support and in V5R20's Q2 2010 update will feature unique comprehensive support for composites design attributes and functional tolerancing and annotation data. Q2 2010's update to the entire V5 portfolio will also include support for Windows 7.

    Luxion, makers of advanced rendering and lighting technology, announced the first release of KeyShot, an interactive raytracing and global illumination program that brakes down the complexity of creating photographic images from 3D models. KeyShot supports many native file formats, including SolidWorks, Rhino, SketchUp, Obj, IGES, and STEP. KeyShot is the replacement for the HyperShot software, the first interactive raytracing and global illumination program, also developed by Luxion. KeyShot is the realtime ray tracing program formerly know as HyperShot. Luxion will provide a free upgrade to all existing users of HyperShot. Pricing for KeyShot starts at $995, while KeyShot Pro sells
    for $1,995. KeyShot is available for immediate purchase for both PC and Mac from

    A Utah design team used its metalworking experience and SolidWorks to create a skeleton sled for an Olympic racer in a fraction of the time and for tens of thousands of dollars less typically required to produce one of the highly specialized sleds. A skeleton sled is a compact racing vehicle that riders steer down high-speed ice tracks by flexing and shifting their bodies. Suddenly without a working sled late last year when hers was damaged, U.S. Olympic team member, 2005 and 2007 World Cup champion Noelle Pikus-Pace, turned to her husband, Janson Pace, an industrial designer, and his employer, NuQuest, a design, engineering, and manufacturing company. NuQuest produced the sled in four
    months, which is much less time than it usually takes to perfect a new design. NuQuest co-owner Troy Beckstead estimated that SolidWorks Simulation saved the company “tens of thousands of dollars” in development costs. Pikus-Pace will use the skeleton sled at the Vancouver Olympics.

    ANSYS, Inc. announced that Volkswagen AG has signed a master agreement with ANSYS and intends to widen its use of ANSYS' comprehensive engineering simulation software. The strategic decision to use ANSYS software was due both to the bandwidth of applications that can be addressed as well as to the innovative ANSYS Workbench platform that allows for a substantial process compression. In its research and development, Volkswagen uses structural mechanics, fluid dynamics and explicit analysis tools from ANSYS to perform, among other applications, studies on climate control, headlights, and engine internal flow.

    A growing number of refrigeration and cooling companies are designing their machinery with Autodesk Inventor. Companies such as Mammoth-WEBCO Inc. (Mammoth), a leading custom HVAC operation, and KYSOR Panel Systems (KYSOR), a leading developer of walk-in coolers and freezers based on innovative insulated panels, use Inventor software to go beyond 3D design to Digital Prototyping. By using Inventor software, Mammoth, which manufactures large-scale commercial custom rooftop equipment that weighs up to 60,000 pounds per section, no longer needs to construct physical prototypes and experiences far fewer errors when manufacturing its massive equipment. Since implementing Inventor software,
    Mammoth has helped reduce manufacturing time by nearly 15 percent and now saves anywhere from $500 to $9,000 per project. KYSOR has streamlined much of the engineer-to-order process for its insulated panels by using Autodesk Inventor and Autodesk Vault software. KYSOR panels are used for food storage in supermarkets and convenience stores, as well as scientific applications where environmental control is critical and cold storage facilities where temperature, humidity, and light must be precisely controlled. With Inventor software, KYSOR says it has increased the overall efficiency of its design automation by about 45 percent.

    Jeffrey Rowe is the editor of MCADCafé and MCAD Weekly Review. He can be reached at or 408.850.9230.

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    -- Jeff Rowe, Contributing Editor.

    Review Article
    • CFD: Don't be Scared March 06, 2010
      Reviewed by 'John Chawner'
      Thanks for giving mesh generation top billing (or at least equal billing) with CFD in the recent article "CFD: Of Meshes and Math". Products like Mentor Graphics' FloEFD and Blue Ridge Numerics' CFDesign (among others) are helping make CFD more accessible to design engineers (aka non-expert analysts).
      But I have to take minor issue with the tone. This whole "fluid dynamics is hard" business reminds me of Barbie's "math is hard" but without the corresponding outrage. Yes, engineering *is* hard. That's why we go to school for 4 (or many more) years to become adept at it. Yes, CFD is hard but so is FEA (which also requires a mesh) but no one thinks twice about pounding out a bunch of FEA simulations. Yes, some engineers don't fully get CFD and then others of us (like me) get the "deer in the headlights" look when presented with a structural fatigue problem.
      Stepping down from the soapbox, I agree with your assessment that CFD will continue to grow as the overall use of computational simulation increases. After all, simulation during the early stages of design leads to all sorts of good things including better products and quicker to market. And, mesh generation will be a driving factor in making use of CFD more efficient and effective. After all, your simulation is only as good as your grid.
      Thanks again for some superb insights.
      Full disclosure: At Pointwise we deliver mesh generation software and services to CFD practitioners worldwide.

        2 of 2 found this review helpful.
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    • NICE FOLLOW UP! March 03, 2010
      Reviewed by 'Russ Henke'
      Dear Jeff:
      Thanks for your MCAD Weekly piece on "CFD: Of Meshes and Math". You caught the mood perfectly of many of us mechanical engineering students in our undergraduate years in fluid mechanics classes.
      You're article was an excellent follow-up to the November 09, 2009 EDA Weekly posting of "MAD Progress":
      Keep up the good work!
      March 03, 2010

        One person found this review helpful.

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