bowl.0768

This is a benchmark curvilinear tank case for testing the (super)generalized elevation equation. See also trap.1600. The domain has dimensions shown below.

This domain is discretized using 768 quadrilateral elements, and 813 (1626 space-time) nodes. The smallest element length is initially 0.25. The mesh was generated with the "Mesh2D" program. Click on the image below to view a PDF view of the mesh, with element and node numbers included.

The MIXD format (space-time) mesh files for this geometry are here:

minf mxyz mien mrng

Run A

Start from still water and hydrostatic pressure. Ran 200 steps with β = 0.5 and τ_DC = 0.0. Too much shear at the wall leaves a sharp (one-element thick) trail of fluid, leading to too much deformation eventually? Time step size of 0.1. Data and logs taped on OHIO.

Run B

Same as Run A but with τ_DC = 0.1. Ran 500 time steps with good convergence, but the trails are still there. Data and logs taped on OHIO.

Run C

Same as Run A but with β = 0.1. Ran 500 time steps with good convergence, and good solution. Mass conservation within 0.1 %. Time step too small (wasteful)! The period of the excitation is about 6.0, so a time step of 0.25 should be more than sufficient. Data and logs taped on OHIO.

Run D

Same as Run C but with time step size of 0.25. Ran 4000 steps. Height (i.e. not the elevation φ but coordinate y) at the two upper corners:

The coordinates were recovered in EnSight, creating y variable, and using Query tool to extract value of y at nodes 813+314=1127 (left) and 813+813=1626 (right), and then saving that data to a text file, which was later fed into "Gnuplot". Also made PS files of streamlines, limit -1.0 to +1.0, at steps 300, 340, 380, 420, 460 and 500, corresponding to records 61, 69, 77, 85, 93 and 101, and time of 75.0, 85.0, 95.0, 105.0, 115.0 and 125.0.

Run E

Same as Run D but with excitation amplitude of 0.15. Mesh tangled after 3949 steps.

Run F

Testing.

Run G

Rerun of Run D with new XNS. Animation of stream function and velocity vectors is shown below. Click on the frame to load the movie.

Animation notes: Volume mesh colored with stream function, limits -0.6 to +0.6, black velocity vectors scaled by 4.0 with "normal" tips of fixed size 0.05. Animated 800 time steps. Imported at 15 frames per second.

Run H

Navier's slip condition replaced with BC-free condition on slip boundary to fully elliminate tangent stresses. Ran 4000 steps with no recirculation and good mass conservation. Used 4 nonlinear iterations to save time. Animation of stream function and velocity vectors is shown below. Click on the frame to load the movie.

Used in bibRef(Behr2003a).

Run I

For comparison with Run H, removed Navier's slip condition and did not use BC-free condition. Ran 4000 steps with recirculation observed, but also insufficient convergence (and mass gain). Insufficient number of iterations?

Run J

Same as Run I, but with 8 iterations per step. No visible change from Run I.

Run K

Same as Run G, but with only 1 outer GMRES iteration, for better comparison with Run H. Used in bibRef(Behr2003a).

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