Making errors stable

Mihail Galabov

Hi everybody,

I am making computations with my own code over a flow of viscous fluid (spinning a glass fibre) using a grid by the distance. My goal is to reach stationary solution starting from an "approached" one , so this is a non - stationary case because I'm making steps by the time. The problem consists of the unability to improve the precisity of equations by making the computational grid thinner. The results of my test , based on Runge evaluation method for consecuently included one in another computational grids, gave horrible results. So I came to the conclusion that there is some kind of additional error of approximation in the scheme that has nothing to do with the way of approximation of the derivatives from the differential equations , but with the physical essence of the problem. The method I used to avoid this "additional error of approximation" is based on transportation of fluid particles along the flow. This method makes the practical row of approximation error stable along the whole length of the flow even at time when there are still non - stationarities in the process. This made the practical and the theoretical (O(h2) because of the central differences) errors equal. This was an amasing result for me. It made me able to improve my precisity of equations and to achieve good precisity even at small number of points in the computational grid. The method can be applied not only in my case but in all cases of computational fluid dynamics when there is some kind of flow.

Can someone tell me something about this problem ? Is the stability of errors a real problem of the computational fluid dynamics and how is it solved?

Yours, Mihail.