Disclaimer I'm an applied mathematician by training, not an engineer. My work research primarily focuses on creating new "methods" to solve different PDE's related to solid deformation (elasticity) and fluid mechanics. In this sense, i know how to solve a pde problem computationally. From my perspective, engineers use my work as "tools" to accomplish their work.

However, due to my lack of education/experience in engineering, i admit i'm actually rather clueless on how numerical solutions to pde's are really used in an engineers actual practice. The primary source of my confusion is the following:

I've been told that engineers never (or should never) conduct numerical simulations (e.g. finite element analysis, CFD, etc...) without knowing or having a good idea ahead of time what the simulation "should" look like. This helps engineers discriminate realistic results from questionable ones.

However, i argue that if the engineer already knows what is supposed to happen in the simulation, then what's the point of simulation in the first place??? I've always assumed that simulations are needed for predictive purposes, which assumes ignorance of what is to come. That is, I think of a simulation as a stand-alone tool to predict the future when you don't know what to expect.

What i'm looking for is a broader perspective into how/when/why engineers use numerical simulations like CFD and Finite Element Analysis, especially if good engineering practice dictates that you should already know what to expect when you're simulating?

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    $\begingroup$ Probably good engineering practice is only to approximately have a feeling which outcomes would be reasonable and which outcomes would be unphysical. Knowing the result before you do it would probably be asked for too much. $\endgroup$ Commented Feb 3, 2015 at 16:37
  • $\begingroup$ Using simulation you can verify that your design is correct. Alternatively, you can deduce that either your design is faulty, or you botched the simulation parameters. $\endgroup$
    – SF.
    Commented Dec 1, 2017 at 15:34
  • 1
    $\begingroup$ As someone who uses casting simulation software on a regular basis, I have a really good intuition for the general shape of solidification profiles just by looking at a CAD geometry for a few seconds. However, convincing others to make business decisions requires more proof than just "my gut says..." $\endgroup$ Commented Dec 1, 2017 at 16:36

8 Answers 8


I have written mostly about CFD in this answer, however same points should also work for FEA or other simulation techniques.

CFD is mostly used for design optimization and parametric study of the design. Following are a few examples showing how engineers use simulations

  1. Selection of a design: Read: A conceptual study of airfoil performance enhancement using CFD. This thesis shows use of CFD for selecting the best design out of a number of candidate designs. Engineers often go for simulations to select 'the one' out of many.

  2. Shape optimization using CFD: This paper gives an example of wing shape optimization using CFD. And this amazing YouTube video is an excellent example of the way an engineer would use a CFD software (OpenFOAM) and genetic algorithm. CFD makes it possible to arrive at a better design without actually building a number of prototypes and testing (which is an expensive and long process). Actually design optimization is the most common way the CFD is used. According to this survey, mechanical design engineers make the use of CFD the most (note: I do not know the authenticity of the report).

  3. Using simulations where experiments are difficult to carry out / might cost a lot of resources (or life): Applications where experiments are not possible to carry out, such as the heat transfer in hypersonic re-entry vehicles (examples here), or blood flow in human body, can be simulated with a computer and final design can be tested. Another example; CFD is used for placement of probes on a wind tunnel model. CFD gives, for example, the position of the stagnation point on a surface of the model, and there we can have the pressure probe placed and then test the model in actual wind tunnel. This presentation explains how CFD and wind tunnel are complimentary to each other. Also CFD is used to predict the results where experimental results are not available (one can not have probes everywhere on the model).

  4. Design and optimization of the experimentation facility itself: Simulations are commonly used for design of the facility itself. For example, this report describes how CFD is used for design of the wind tunnel.

  5. To develop a theoretical model: This is often seen in cosmology. Scientists carry out simulations based on a model and validate with the experimental data. This iterative process results in better understanding of the physics and working of the universe. NASA astrophysics group have done some simulation of Supermassive Black Holes, this video talks more about it.

  6. In movies, art and animations: This question and following answers on Scicomp.SE show, how much a role CFD has to play in movies and animations... (disclaimer: I have asked the question).

  7. Some other applications: Aerodynamics of the insect flight, Noise computation using CAA, design of antennas and stealth technology using CEM, Applications of CFD in food industry etc.

The list will go on... End of the day, CFD is a virtual wind tunnel, its a workbench where an engineer can test his idea without manufacturing / building anything. So if the results are validated against a known model / experiment, then one can rely on the CFD methodology for a slight change in geometry or shape. Also because of the CFD results, an engineer can have confidence in his/her experimental results. Thats why the term validation. A good resource for validation test cases here.



To summarize the other answers: An engineer needs to know qualitatively how the simulation will go, but he still needs to run the simulation to get the quantitative answer.

Also, simulation allows the engineer to vary the parameters slightly (Monte Carlo simulation) in order to evaluate the stability or margin of error of the solution. This is frequently done in electrical circuit simulation, for example, in order to evaluate a design's sensitivity to component value tolerances.


Engineers should have a general idea of the expected result (Balpark values, expected behaviour)when using a complicated computer model. Most of the time these conclusions are based on a (much) simpler model, that preferably can be checked by hand.

Biggest reason for this is to eliminate the possibility of human error in constructing the model itself. Using modeling software as a black box is seriously frowned upon and considered very unprofessional and risky. When results are very different from the expected, the first question one should ask is 'is the model well constructed?, didn't I make a (stupid) mistake?'

A second reason is to gain control of the model by understanding it. The simpler model acts as a stepping stone in the understanding process. When a model is understood it is easier to know what to change to find the solution to the engineering problem. As such the model is a tool in the design proces.

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    $\begingroup$ This is a great point. Just the simple process of building the model often leads to deeper understanding of a new problem. $\endgroup$
    – Rick
    Commented Jan 26, 2015 at 19:44

As my Fluids lecturer said many years ago, “if the mathematics doesn't agree with reality the mathematics is wrong”. You can easily substitute the words model, theory or simulation for the word mathematics..

Engineers who use simulations should have a very good idea of what to expect for a solution, not necessarily know what the answer will be for a simulation. There is a difference. That's where the engineer's experience is critical and why inexperienced engineers should always be well supervised when doing simulations.

Engineers use simulations for a variety of reasons, depending on the field of engineering they work in and what they are doing. Some engineers use simulations to confirm their designs while others use simulations to look for potential weaknesses in designs or materials.

The other aspect of simulations is they allow engineers to consider a number of “what-if scenarios” to ascertain what could happen when parameters are changed. This can be used to look at upper and lower bound performance limits or it can lead to design changes and in some cases a total redesign.

Again, depending on the field of engineering, simulations are also useful when considering when something need to be added to or increased in scale, such the affect on a water distribution system by adding a new development, or changes that need to be made to the ventilation system of an underground mine.

Simulations can also be done to look at: - the impact on the flow of materials and resources: oil or water in their respective piping networks, air in ventilation networks, ore from a mine or several mines to a processing plant or a number of processing plants - blending of mineral products extending public - transport infrastructure like railways, road, electricity & communication networks - traffic movement when changes are made to a traffic system: road blocked or widened, reorganized for one-way traffic, the introduction of clearways and the prohibiting of parking on the sides of roads the - the design of underground spaces for civil applications such as
underground parking areas, train stations or tunnels and stopes in an underground mine. - financial NPV evaluations for project economics and investment purposes

It's always cheaper and prudent to run a number of simulations than to construct something and have it fail catastrophically.

As another one of my university lecturer's also said, way back when, “Doctor's bury their mistakes, architects plan vines around their mistakes, engineers are killed by their mistakes”.

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    $\begingroup$ "If the mathematics doesn't agree with reality, then the mathematics are wrong"... I whole-heartedly agree with you. I wish other mathematicians felt the same way:) $\endgroup$
    – Paul
    Commented Jan 24, 2015 at 17:47
  • $\begingroup$ Our notion of reality changes every day! And yet mathematics never does... I guess maths in its own is quite interesting. We can choose to relate it to our perception of reality though! $\endgroup$
    – Subodh
    Commented Jan 24, 2015 at 17:57
  • $\begingroup$ If the mathematics doesn't agree with reality, it doesn't mean the mathematics is wrong, it means it is wrong to apply that bit of mathematics to that real life problem. Models can't be wrong, they can only be inapplicable. $\endgroup$ Commented Apr 17, 2022 at 18:21

In my particular field (buried culvert design), we run finite element analyses constantly. We almost never change a design based on the results; we know going in (from a variety of factors, mostly prior experience and conservative assumptions) whether or not the design is good. We run the analyses to demonstrate to others that our design is good. We may tweak something, but it is never changed substantially.

Very often, building codes and regulatory agencies specify certain requirements for demonstration of design acceptability. Sometimes running the model is more-or-less jumping through these hoops, so that a person with less knowledge and time can quickly ascertain the relevant facts without getting bogged down in the minutia.

To summarize - and it's not my intention to be glib, but:

Engineers use FEA/numerical simulation so we can have something to present in a courtroom other than the contents of our brain matter.


In our reports, we also like (and our insurance carriers REALLY REALLY like our) being able to say "The model says...".

  • 1
    $\begingroup$ I never imagined it this way.. ! So how much does the quality of simulation matter in such cases? I mean grid spacing, timestep etc. BTW, since it is a completely new perspective to look at a simulation, +1 $\endgroup$
    – Subodh
    Commented Jan 26, 2015 at 20:20
  • $\begingroup$ Quality (which by your description I take to mean accuracy) is of varying importance - it has to at least be good enough that a person of comparable knowledge would say you have lived up to the standard of care inherently required when you put your stamp on your report. But sometimes too much quality/accuracy is a real concern; it can make it look like you know more than you do, or that you are saying that you know more than you do. You have to be very careful and always be managing your liability side (or you won't stay in business very long). $\endgroup$
    – Rick
    Commented Jan 26, 2015 at 21:14
  • $\begingroup$ Another issue: it's often too expensive to run multiple analyses. The time requirement is just too high. For this reason alone you would endeavor to NEVER invest the time in building a model that you aren't already very certain you will end up using. $\endgroup$
    – Rick
    Commented Jan 26, 2015 at 21:35

I design electric motors and I use electromagnetic FEA as part of that design process. Motor designers have a lot of good analytic techniques that get us very close to the actual performance of the motors for certain key parameters (torque, current draw, speed, etc.). However, this requires that we make certain assumptions that may or may not be valid. For example, I might assume that the flux through a certain path of steel is evenly distributed or I might assume a certain amount of flux leakage through a slot. Those types of assumptions are often totally valid ones to make. One reason I use FEA is to confirm that the assumptions I made were valid. If they are valid, the FEA results will give me pretty much what I expected. If they aren't valid, the FEA results will help me figure out what my bad assumptions were.

Another reason I use it is that there are some motor parameters that can't be determined very well using analytic techniques. For example, torque ripple (the amount of variation in torque as the rotor rotates) is difficult to do with analytic techniques. I know certain motor types have worse ripple and I know certain combinations of poles to slots has better ripple than other combinations and other rules of thumb, but FEA can help you quantify that.

The other reason I use FEA is to really fine-tune a design. If I have a design that pretty much does what I want it to, I can then try to get the efficiency up a bit or reduce the magnet thickness or whatever.

So, I use it to 1) check my assumptions, 2) solve problems that can't be done easily with analytic techniques and 3) fine-tune my designs to increase performance or decrease cost or just make it better. All 3 of these require that I have a pretty good handle on the design before I start the FEA process. That doesn't mean I'm never surprised by the results or don't learn things, but when those surprises happen, you can be sure I'll be going back and trying to figure out what went wrong.


To give you a practical example: my dad was a structural engineer working for a large national company; his specialty was to take the drawings for constructions (mainly building facades), which usually were reasonable "OK", and calculate specific things like size of screws/bolts, spacing, necessary dimension of struts and so on. They worked on very large structures, like airports, opera buildings, skyscrapers. A little change in calculation (say, screws which are a bit smaller, or a bit fewer) can mean hundreds of thousands of € saved. Too small, and bad things happen.

In his last decade before his pension, he mainly used GWBasic (!) with little self-written programs for his work. This means, he directly worked the methods he knew and had used long before the advent of computers in his field into GWBasic programs. You could call this some kind of trivial numerical simulation, but in fact it was just a glorified pocket calculator (actually he had done the same on pocket calculaters with programmable magnetic strips, before).

At the end of his working days, professional Finite Element software started to appear, and he used those for very complicated projects from time to time. It was never about actually coming up with new results, but always to find out whether a certain approach was feasible. I.e., in his line of work, it's all about loads on steel bars and such; and the manual calculations are, for obvious reasons, mostly reduced to linear cases (and then with 100-200% security margins added to that). Finite Elements opens up whole new worlds for architecturaly interesting buildings.

With the Finite Elements, he could get much closer to real necessities (or so people believe), but obviously now it is hard (or, for people like him) outright impossible to verify the results. And believe me, "risk" is a very prominent thing in that respect; if the facade of a big building in a city comes down, people die and engineers end up in jail.

TL;DR: Engineers use numerical simulations similarly to physicians/scientists, to verify assumptions, or iteratively find sweet spots and such. But it is very much required that they need to know what, in general, to expect. It's the same as in science, where an experiment for which you did not reason about the expected results beforehand, is just junk.


There isn't much left to say but that knowing result before runing simulation isn't knowing exact numerical value but to have certain expectations regarding solution based on understanding the physics of the problem. Usually engineers set problem and choose general method and when we finally formulate problem as set of equations and boundaries we seek help from mathematicians to help us solve it in most effective way. Usually engineers are those who define equations, mathematicians solve them. If you have no understanding of bending than, though you can solve biharmonic equation, your solution will Probably not be set of right deflections. When mathematician learnes to use tools for solwing pde he can solve most pde problems but eg. mechanical engineer though will understand basics of solwer will not try to use it to solve radar imaging or electric flow.

  • $\begingroup$ The only way most, if not all, CFD problems are solved is due to the judicious use of assumptions to reduce the unknowns... $\endgroup$
    – Solar Mike
    Commented Dec 1, 2017 at 14:58
  • $\begingroup$ Same as structural and other. Last few weeks I've been solving bending, the biggest problems for me are boundary conditions. $\endgroup$
    – Katarina
    Commented Dec 1, 2017 at 15:57

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