John C. Chien

June 10, 2000 18:38 
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.
