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Tom July 13, 1999 14:21

Unsteady Calculation
Hello, I try for the first time an unsteady simulation of fluid flow. Now I do not know how large a typical time-step is. My volume has a length of about 300 mm and the typical velocity is about 15 m/s. My calculations are done with fluent, seperated, implicit. I tried a time-step of 0.001s. The solution converged (residuals smaller than 0.001) in one or two iterations each time-step. 1.) Is the time-step too small, or do I have to reduce my convergence-crit. ? I feel, but I don't know, that the convergence-criterion (residuals) from a steady flow cannot taken for an unsteady one. 2.)What influence has the length of the time step to the result at time t ? I heard, that you get different forces at the same time on your monitors (middled wall-shear-stress) with different time-steps. Thanks a lot

Sung-Eun Kim July 13, 1999 22:29

Re: Unsteady Calculation
Dear client,

An idea of appropriate time step can be obtained if you have a rough estimate of the characteristric time scale of the unsteady phenomena you want to resolve. For example, when you try to simulate vortex-shedding around a circular cyliner, it helps a lot to know in advance approximate shedding frequency. Typically, you need at least several scores of time steps to cover one period or chracteristic time scale, although you may be able to use less number of time steps if you use high-order temporal scheme. Having said this, I mus add that it only gives you, at best, a rough estimate of time increment. To ensure that you properly resolve the characteristic time scale of the flow in question, you need to investigate the effects of time step size by trying several different time steps.

John C. Chien July 13, 1999 23:37

Re: Unsteady Calculation
(1).It sounded like that you were driving a car without a license! (2). On a straight highway, you may be able to hold the position of the steering wheel steady for a few seconds and still be able to stay in the same lane. This is more or less like the running the steady state code. (3). If you are driving down-hill on a winding mountain road, I am sure that you will disappear into the deep valley. To stay alive, you will have to move the steering wheel constantly. That rate of moving the steering wheel depends on the road conditions. (4). So, to be on the sure side, you should move the steering wheel all the time for any road conditions. I can't teach you how to drive, but that is just the principle. (5). I remember that was exactly how I drove when taking the driving lessons many years ago. Later on, when I became familiar with the road conditions, I was able to relax and move the steering wheel only when necessary. (6). You don't try to run a transient code just to get the converged steady state solution. To get accurate transient solution, make the time step as small as possible to avoid running into a tree.

Tom July 14, 1999 01:26

Re: Unsteady Calculation
Thank you John. Well John, I think in this case your point 1.) is correct, but every cfd-engineer had someone done his first unsteady calculation in order to get the license :)

If you make the time-step as small as possible you still have the problem of convergence. What's the "definition" of convergence in one time-step: The residuals don't change anymore (as used in steady calculations), or: the residuals must have a special level (and they still decrease) ? to your point 6.) I use (because of the possibility of larger time-steps) an implicit sceme. I thought, it is possible to "run into a tree" with the explicit sceme, but not with the implicit one.

John C. Chien July 14, 1999 08:12

Re: Unsteady Calculation
(1). In the explicit methods, you use the existing solution as the sole known initial data to compute the next time step solution. Once the next time step solution is obtained, it becomes the initial data for the next time step again. This is the situation like driving a car. So, there is no such thing as "convergence" issue. Every operation is one-to-one algebraic. All you need to do is to keep the time step as small " as possible". And as you know that, if the slope is steep, and the time step is not small, sooner or later you will run into a tree. (2). So, your problem apparently come from this "implicit" method you are using. In addition to that, you are probably using a pressure-based method. pressure-based method is derived from the incompressible flow formulation and the pressure is decoupled from the momentum equations into a separate loop. In this approach, you first work on the pressure loop to get some pressure information or correction. Then that information is used in the momentum equations to obtain the velocity solutions. Since this is a pressure field guessing game, you have to go through it many times until the pressure and the velocity field is consistent and converged to satisfy the continuity equation. If this loop ( sometimes it is called internal loop ) is not converged, you simply do not have any solution at all!. So, strictly speaking, you are talking about the convergence of the inner loop. (3).It is important that you do read the description of the method used, because everyone has his own invention. It is hard to know the exact method used in a code by reading the word used. (4). The implicit method is a different way of driving a car. You first drive the car for one second ( or any time step you like), stop the car, get out of the car, and make a survey of where you are. After that you re-calculate some numbers and backup your car to the previous location. Then start the car again and move forward with the new information. ( this is how you get the impression of avoiding the tree because by now you have some information about the location of the tree) This is one way ( a more complicated way) to avoid hitting a tree. (5). The added advantage of using this implicit method is that "you are now asking questions". You can't get something for free. So, you really have to talk to the person who invented your implicit method. The common mistake people make is "they try to understand the inside of a black box". The black box code is the one for you to use, it is not the one for you to ask question about its internal design. (6). So, the simplest way to use a black box code is to compare your results with other test case results. If they match, who care about the one-iteration to convergence.

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