Effect of Element Size on Flow Solution

The purpose of this project was to investigate the effect of element aspect ratio and thickness on a flow solution. To do this, flow past a cylinder was solved at various element sizes using the Navier-Stokes equations for incompressible flow. In this project, Ms. Corfeld was helped by Mr. Yasuo Osawa, at that time a PhD student supervised by Tezduyar.

Full Mesh Around Cylinder
Close up of Mesh Around Cylinder

Procedure

For each simulation a 3-dimensional cylinder model with diameter=2 was used. The mesh, comprised of hexahedral elements, was only one layer thick so a 2-dimensional solution was obtained. For each model the number of nodes and elements differed. For the mesh shown above (radial length = 0.005), the number of nodes=10822 and the number of elements=5260.

The first simulations were computed with Re=140 to obtain a time periodic solution. A steady state case was then run at Re=28. For each simulation the circumferential element length remained constant while the radial element length was modified.

Flow Past a Cylinder

Time Periodic Solution

Steady State Solution

Results

In analyzing the results, the focus was primarily on how changes in element thickness affect the drag experienced by the cylinder. The following plot shows how the average drag differs with element thickness for the time periodic case.

It was difficult to draw conclusions from this plot of the time periodic solution. There is a clear constant region of points that are considered "good", but it was difficult to say what was happening on either side of this region. To determine what was happening, the standard deviation of the maximum drag for each time periodic solution was calculated. Large standard deviation indicates a nonperiodic solution and the calculated average drag can not be trusted.

To eliminate the factor of time, simulations were run at Re=28 for a steady state solution. The following is a plot of average drag vs. element thickness for the steady state case.

Conclusions

Combining both the time periodic and steady state solution and the standard deviation plot, we were able to determine which points produce sufficient accuracy in the flow solution. As the mesh becomes too coarse the solutuion is stable, but accuracy is lost. As the mesh becomes too fine, it becomes difficult to obtain a periodic flow solution. As shown by a comparison of the time periodic and steady state cases, effective mesh size differs with Reynold's number.

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