convergence
 

Hello everybody I am Luca an Italian engineering student. Sorry to bother serious workers like you but sometimes it is really difficult to learn something in the Italian universities. I can not understand how the SIMPLE algorithm checks if the solution is converged? In the book we use the author talks about "continuity errors (inflow minus outflow) for each cell", what is that? And how the algorithm links the errors for a variable on a cell to the errors on the whole domain? And then how does the algorithm link the error for a variable with the errors for the other variables (I suppose it should do it)? If I set a too high convergence "change for the variable" (e.g. 10 e+1) in the TDMA is it possible that the SIMPLE will never converge? Anyway my ideas are very confused so if you want to help me I would be very grateful! Thank you Luca

Re: convergence
 

Hello I'm mehdi for Tunisia, Mr Luca you must see the book of Malalasekera and Versteeg : "An Introduction to Computational Fluid Dynamics:The Finite Volume Method", They explaine all about the Simple algorithm of Patankar.

Re: convergence
 

(1). In iterative solution, you are trying to correct the current guess value to give you improved guess value, so that the improved value will eventually represent the correct answer. The correct answer is the one which will satisfy the local and global conservation law, and the continuity across the cell is one such condition. (2). In most cases, this is not possible, either due to poor initial guess, the sensitive algorithm to improve the old value (guess), or the incorrect parameters used in the iteration process. So, we have to adjust these parameters to control the rate of change of improved values, in such a way that it will zoom in the final correct result. (3). So, there is nothing unusual about the divergence of a solution. And in many cases, the poor mesh alone will prevent one from getting the converged solution, not to mention other factors such as the initial guessed value, the boundary conditions, etc. (4).A simple example is to find out the age of each student in a classroom. The initial guess can be one year old for every student. Then you can ask each student an indirect question related to his or her age, and then calculate the improved guess of age. Then you can check the age difference between two neighboring students, or the total sum of students in the classroom to see if the number is within certain limit, etc... (5). It happens that the method you mentioned isolates the pressure terms from the momentum equations in the iteration loop. And the pressure is updated in a separate loop. As a matter of fact, there are many ways one can do to update the pressure in the isolated loop. (6). But regardless of what you use,at any stage of iteration, all you have is just some kind of improved guess. These improved values do not satisfy locally, or globally the conservation laws, until the converged solution is reached. In other words, there are always errors locally or globally. Errors in continuity equation means that mass is not balanced across the cell. (7). And if your improved guess of the age of a student changes from iteration to iteration, then you know that you have not reached the correct age of the student. But if you set the convergence limit to 100, then the first initial guess will pass the convergence test. On the other hand, if the limit is 1 year, it will be very difficult to converge.