#meshgeneration

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Guts of CFD: Navier Stokes Equations

Navier Stokes Equation. Shrouded in mystery and intimidation. Navier Stokes is essential to CFD, and to all fluid mechanics. This equation defines the basic properties of fluid motion. But there is more to gain from understanding the meaning of the equation rather than memorizing its derivation. Today we review Navier Stokes Equation with a focus on the meaning behind the math.

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[runewake2]

Lets build a basic colored voxel "chunk" from start to finish! We'll focus on constructing three main components: a Chunk which stores data about the world, A ChunkGenerator which fills the Chunk with initial information (it builds the world) and a MeshGenerator that converts our Chunk into a Mesh you can see. This isn't necessarily an efficient implementation (actually, I can assure you it is not) but hopefully we can set up a strong foundation to build and expand from into really cool new problems. By separating the generation of our Chunk from the generation of the Mesh we can modify either the Mesh or World generation independently with minimal overhead making expanding and adding onto this foundation simple. There is still a LOT that is not in this implementation. Half of our triangles are generated with the wrong Vertex winding causing them to appear backwards, we have no normals configured so lighting doesn't really work either. There is also a pretty significant mistake where we regenerate our mesh once for every single cell in the Chunk. For a simple 10x10x10 cube that will result in 1000 mesh generations even though we just need 1. My bad! We'll fix that in the next video in this series. There are a lot of places we can take this, if you have any ideas or suggestions let me know or take the code your own path. Let me know in the comments or join our Discord to walk through any problems you run into. You can browse the code from this video on GitHub: https://ift.tt/2L32kWA Come Join the World of Zero Discord: https://ift.tt/2txCKO8

[dmsonline]

What is CFD

Introduction to Computational Fluid Dynamics

https://youtu.be/jQHp49OyPn8

1.0 Introduction

We live in a world of motion.  In this world, every movement that you make interacts with fluids. Walking down a corridor, air flows around you.  Your body heats the air over your head, which rises to the ceiling.  A ship turning in a channel gets driven by water flow around the hull and rudder.  Every aspect of change in our world gets shaped by fluid mechanics.  Given its pervasive presence, we need the ability to predict and control fluid mechanics.  One of the best tools in the arsenal is computational fluid dynamics (CFD).

2.0 Methods of Analysis

CFD works best as one of many tools available for analysis of fluid mechanics.  These divide into three major categories: Analytical Computational Experimental For analytical methods, imagine someone at a chalkboard, white dust on their trousers, deriving lengthy, complicated hand equations.  But hand equations still remain too simplistic to be accurate for anything but the most basic of scenarios.  On the other end lies the experimental, requiring expensive testing facilities custom built for detailed experiments. (Figure 2‑1)  Plus, these facilities are often targeted towards specific types of problems and experiments.  So we can only test for known theories and designs.  They restrict our ability to explore new possibilities.

Figure 2 1: Example of Wind Tunnel Experiment   Computational methods offer a happy medium.  They work like experimental methods, but we construct virtual test facilities on the computer.  No construction costs, and infinite flexibility to customize the experiment for each purpose. 

3.0 The Solution of CFD

3.1 Fluids Are Complicated

The problem behind CFD was that fluids remain complicated.  The mathematics to describe the physics of fluid mechanics get very messy.  There was an anecdote that Albert Einstein one day sat down to try and derive the fundamental equations for fluid mechanics.  After many weeks of intense frustration, he gave up and pronounced it at too difficult.  He moved on to other easier tasks . . . like special relativity.  Sure, this was just a tall tale, but it explains the problem of fluid mechanics.  We needed a way to simplify overly complicated mathematics, but keep them applicable to the real world.

Figure 3 1: Albert Einstein

3.2 The Answer of the Box

The solution was a box.  By applying the fluid dynamic equations to the very simple geometry of a cube, the equations became manageable.  Imagine a simple cube of fluid where you knew the fluid flow properties on every side (Figure 3‑2) Combine this with the simple geometry of the box, and the equations for fluid mechanics become manageable.  Still intensely complicated, but now simple enough for a human to program and a computer to solve.  We can now predict everything about the fluid flow for any point within that box.  This was the basic unit of CFD:  a single cell.         The real magic happens when we start stacking thousands and millions of these cells together, in any generalized pattern necessary.  CFD became a generalized tool:  create a generalized physics solver it to literally any shape of geometry. 

Figure 3 2: The Box: The Basic Cell of CFD  

4.0 CFD Accuracy

Everyone questions whether CFD can be trusted.  Wrong question.  The software and methodology are only as good as the CFD engineer that operates the software.  Yes, the software possesses great potential, capable of extreme accuracy, even matching the capabilities of experimental methods.  But the CFD engineer must demonstrate and prove that accuracy for every single CFD project.  The accuracy lies in the CFD engineer, not the software.

5.0 Conclusion

CFD is not a magic bullet; it adds to our toolbox in fluid mechanics analysis.  We don’t throw away all the other tools as a result.  That being said, this is one impressive tool, when used correctly.  If used improperly, it can become an incredible waste of time and money.   The key rests with finding the right CFD engineer.  The best CFD engineer’s are fluid experts first, and build on that knowledge to efficiently drive their CFD software.  With the right operator, CFD can be cost effective, incredibly informative, and offer unparalleled flexibility.  Those are the qualities that anyone wants from their tools, and CFD can deliver.

6.0 References

Wikipedia Authors, "MD11 12ft Wind Tunnel Test," Wikmedia Commons, 7 January 2007. . Available: https://ar.wikipedia.org/wiki/%D9%85%D9%84%D9%81:MD-11_12ft_Wind_Tunnel_Test.jpg. . Wikipedia Authors, "Albert Einstein Head.jpg," Wikimedia Commons, 25 11 2014. . Available: https://commons.wikimedia.org/wiki/File:Albert_Einstein_Head.jpg. .       Read the full article

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Guts of CFD: Multiphase Modeling

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Practical CFD Modeling: Judging Convergence

After you start the CFD simulation, when is it finished?  Not an easy question.  The well-trained CFD engineer uses three main tools to judge simulation convergence, and how to combine those tools into a cohesive picture.  Learn about practical CFD convergence.  #CFD #NavierStokes #ANSYS #StarCCM+ #Engineering #Simulation Read the full article

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Guts of CFD: Interpolation Equations

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Guts of CFD: Transport Equation

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Guts of CFD: Navier Stokes Equations

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Guts of CFD: Navier Stokes Equations

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Practical CFD: General Approach

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CFD Workflow

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Which CFD?

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