I have some questions regarding errors in CFD simulation and is hopeful that someone can point me in the right direction.

(1) What kind of error should one consider when presenting a CFD simulation results and (2) how do one calculate/estimate the error(s) in a 3-D FLUENT simulation ?

Many thanks in advance.

1. Errors can come from different sources - You can have problems with your physical models - turbulence models that don't work for your type of flows, combustion models that behave badly, ... You can also have numerical problems, which means that you are not solving the equations/models correctly. This can be due to bad convergence, grids that don't resolve the physics, too dissipative schemes, schemes that gives oscillations, ... In the end you can never be sure that your solution is correct - there is no mathematical way to prove that your solution is really a valid solution to RANS. You need experience to be able to tell if your solution is good or not.

2. It is not possible to do a strict error-estimate on a CFD solution. What you can do is to verify that you don't have any of the problems mentioned above - You can look at residuals to make sure that your solution is sufficiently converged. You can look at conservation of different global properties - mass flow, energy, ... to make sure that you are capturing the global physics. You can also try different models to make sure that you get a similar solution with another model. Another thing to check is that your grid is fine enough - try refining the grid to see if you get the same result. Even if you've done all this you can't be sure that your solution is good, or know how big errors you have, but you can be more confident in your solution at least.

(1). Normally, you need a mesh to do CFD calculations. If the solution is a function of the mesh used, then you will have errors. It is a must that when you present the solution, the solution is independent of the particular mesh you created and used. (2). There is no need to address the absolute accuracy of the results, because within CFD one can use linearized potential equation, full potential equation, Euler equation, parabolized equation, Navier-Stokes equations, etc. As long as the solution of the equation is independent of the mesh and is repeatable, then the solution to that equation is accurate. (3). So, the only way to estimate the error in solution of the equation, is to try a few different meshes and check the solution sensitivity vs the meshes. (4). If you are solving the real world problem, then comparison with the test data is probably the only way to go. Otherwise, CFD solutions are just solutions to a set of equations, including some physical models if required. (5). To make it easier to understand, if your fine mesh solution is different from your coarse mesh solution, then you can say that the coarse mesh solution has higher errors in it.( it is an over-simplified example, so a systematic study in mesh independency is essential. Otherwise everyone will be presenting the 20x20x20 solution, which is much easier to obtain than that of 100x100x100 solution.

"All models are wrong, some are useful." G. E. Box

Be more productive by looking for the use in models instead of spending time questioning their validility.

OK, OK, I know, if the quatitive accuracy is too bad then the usefulness diminishes quickly. Depending on what industry you are applying CFD in you may well be surprised at how innaccurate you can be whilst still finding use in your models, therefore being more a more productive employee, serving your company better and so being a postivive contributer to the human race.

Fred.

I still remeber the paradox quoted in Fluent TG a few years ago: "Nobody belives analysis results except the analyst, everybody belives testing results except the tester" (may not exact). The comments for the Error question have been excellent. I think there are only a few things you can do: 1) Make sure your physical problem is well represented by the mathematical model (equations), 2) Make sure the mathematical model is numerically well converged. 3) Check the model results agains testing data, EXPERIENCE (IMPORTANT)or even the other modeling resutls that you know to be true.

(1). Although there are two distinct phases involved in CFD, the accuracy of the solution is normally related to the mesh used. (2). The numerical methods and the physical modelings are part of the problem solving process, that is the assumptions used. (3). One can assume that the governing equation is inviscid, and try to obtain the CFD solution of the Euler equation. The accuracy of the solution is strictly related to the accuracy of the numerical solution to the Euler equation. In other words, the assumption of using the Euler equation can not be considered as part of accuracy. And sometimes, it is possible to obtain analytical solution to the Euler equation. In that case, the close form solution will be the exact solution with no accuracy problem, while the series representation may have accuracy problem depending upon the number of terms used in the series. (4). Therefore, it is very important to know that the physical modeling of the process is basically the assumption part of the problem solving, not the accuracy part of the CFD solution. This is because the assumption is normally defined in the positive way, that is, the formula used are clearly stated before the solution starts. (5). So, typically in the industrial design environment, there will be solutions to the 1-D equation, 2-D equation, 3-D inviscid equation, and 3-D viscous equation, etc. They are used in the design process at the same time. (6). It becomes clear that whether to use a particular equation or a turbulence model is not the accuracy issue in CFD ( this has been incorrectly identified and discussed in the past in the journals). It is part of the design process itself. (7). This is the reason why we have seen so many failure in the CFD applications in the design process. (8). CFD is not just the geometry and mesh generation, and the design is not just the change in the shape and geometry. (9). A simple example is: if you are an engineer dealing with turbulent internal flows, then you must have knowledge about the turbulence, the turbulent boundary layer theory, the turbulence modeling, the flow separation in turbulent boundary layer. You can take the testing approach to obtain the necessary information for your design problem, you can also take the CFD approach to solve either the boundary layer equation or the full Navier-Stokes equations. This concept is extremely critical in getting a good design. (10). From my point of view (so you can keep your own view point I guess), CFD deals mainly with the numerical solution and the solution accuracy. Once the solution is obtained, it can be used in the design process (or development process, etc...). But the design integration is a separate part, which can use CFD solutions or the testing data, or both. That design part is still the traditional process, except that now the CFD solution is being used. (so, I call it integration) (11). So, if the CFD engineer is responsible for the numerical solution accuracy, and the test engineer is responsible for the test data accuracy, then "who is responsible for the mesh generation method?, solution algorithms development?, turbulence modelling? pre- and post-processing?" (12). The answer is: you need a "CFD development department" and a "CFD application and integration department". (13). Without such organizations, you are going to have a lot of troubles in answering your own questions, such as " I am getting CFD results very different from the test data, is it because of my poor mesh? or the 2-equation turbulence model? or the upwind method? should I double the mesh size? (but I am running out of the machine memory already) should I use a low Reynolds number model? or a two-layer model? or even LES? Is the second-order upwind method good enough? (14). Regardless of what you do (trying to answer these questions, or running the code day-and-night as most companies do), the end result is always bad. (that is you are not getting the good design) This is because those questions should be answered systematically in the CFD departments. (15). By the way, in this message, "you" is the same as "one", not the person reading the message but someone else. Just a minor detail.

Thank you for all your comments on my question. I appreciate it very much.

I am the only cfd user in a research group whose backbone work are mainly physical experiments and from time to time, I find myself having to justify tbe validity of the results of the numerical simulation.

The other reason was certain fluid mechanics journal will no receive papers on numerical work unless some "error analysis" has been done, although it wasn't clear what kind of analysis is required.

Once again, thank you for your time in answering my question. Further comments from other gurus and experts are most welcome =).

LW, (or anyone else),

Can you please tell me where you got your quote, I don't know what the Fluent TG is.

Regards Althea

It was in either Fluent Tutorial Guide or User's Guide (1995 version). I believe it was quoted from some other source by the Guide. Thx!