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  Assignment due dates are noted on the ES 552w schedule. Labs employ provided aPSE template scripts and are to be completed by the class indicated. Prepare your reports using the provided templates.  The Discussion section must include tabular data and plots as appropriate. The Summary must respond to the stated lab objectives.  Archived verification data and extensive lab reports are available at Archived Labs
Student reports can be accessed at Student Labs.
Labs will not be accepted after the archive is opened. 
 
1. Briefly describe a Navier-Stokes problem statement that is of your individual interest. Summarize the form of the "governing" PDE system, its non-dimensionalization, hence non-D groups, BCs and closure model appropriate for your problem. Prepare the report using the online template. Send an e-mail to the instructor when the report is ready for review.
Due at class 3. 
 
2. Recalling the ES 551w unsteady heat conduction problem (last lab exercise), using aPSE determine the sequence of uniformly non-uniform meshings necessary to produce an accurate, hence smooth, solution at t - to = 0.001 hr. Start with delta t = 0.0001 hr, then refine as necessary using theta = 0.5 time algorithm. Reexecute a smooth coarse mesh solution with theta = 1.0, hence estimate the associated time integration error. Replace the GWSh with the FVSh formulation on this (coarse) mesh and compare results. Prepare your report using the online template.
Due at class 8. 
 
3. For the boundary layer 2DBL GWSh, theta = 0.5 algorithm, verify the aPSE template file with the lecture materials. Complete a uniform mesh refinement study for Re = 104, 105, and 106 over some appropriate fixed axial distance xf-xi, hence compare asymptotic convergence to the available theory. With data from sout compare Newton algorithm convergence to theory. For Re= 104, execute a hot wall thermal boundary layer solution, both "up" and "down" via GDOTI, and compare solution profiles to the isothermal case. Repeat one execution using the FVSh algorithm form, compare energy norms, hence speculate on GWSh optimality. Prepare your report using the online template.

As the continuation, verify the 2DBL GWSh templates for the MLT and TKE turbulence closure models, denoted under menu as labs 3b and 3c. Execute aPSE for the model file initial data specification (from the Stanford 1968 Validation Symposium) and graph the resultant predictions including Ret and k and epsilon distributions. If you are curious, experiment with solution adapting the non-uniform meshing as a function of the energy norm distributions. Append the results summary to your report for the laminar convergence study.
Due at class 11. 
 
4. For the 2-D INS omega-psi GWSh algorithm, verify that the template accurately defines the Newton algorithm for isothermal flow. Execute an accuracy/monotonicity study for the driven cavity benchmmark on16x16 and 32x32 uniform meshes at Re = 100. Examine energy norms and integer print fields for solution quality, hence design an improved non-uniform 32x32 mesh based on your data. Proceed to Re = 1000, 2000 and repeat these experiments. From sout, confirm/comment on Newton iterative convergence and automated delta t stepping. Compare solution energy norms as a function of solution adapted meshings, hence validate the conjecture about existence of a "best" 322 meshing. Reexecute one of the poorer Re = 1000 or 2000 cases adding TWSh dissipation (0 <= beta <= 1.0). Compare "best" monotone GWSh and TWSh solution energy norms and their distributions. Prepare your report using the online template.
Due at class 15. 
 
5. For the thermal-omega-psi GWSh algorithm, confirm the quasi-Newton algorithm template construction. Execute the thermal cavity benchmark on 16x16 and 32x32 uniform meshes for Ra = 103 to 106. Examine solution quality and the norms, hence determine a non-uniform "best" meshing for each Ra. From sout, comment on delta t stepping and quasi-Newton (vs. genuine Newton) iterative convergence rate. Rerun the Ra = 105 case with the natural convection non-dimensionalization, i.e. Pe = 1.0, and compare algorithm stability. Prepare your report using the online template.
Due at class 17. 
 
6. For the continuity-constraint GWSh algorithm, verify the jacobians for the aPSE tensor product (TP) and B-matrix, quasi-Newton and the Newton templates. Note in particular the tensor product block tri-diagonal jacobians. Repeat the lab 5 thermal cavity experiment for Ra=106 for an appropriate 32 square meshing. From sout, note iterative performance distinctions resulting from the two quasi-Newton vs. Newton formulations including allowable max delta t step size. Prepare your report using the online template.
Due at class 21. 
 
7. Verify the TWSh INS phi algorithm templates for laminar flow (Newton) and turbulent flow with TKE closure and wall function BCs (quasi-Newton). Execute the laminar entrance duct flow model file for slug inflow at Re = 100, and 1000 for various TWS beta levels. Then restart this solution with beta set to zero and observe loss of stability. Observe Newton convergence and the interplay between phi, sumphi, and pressure in conserving mass flow throughout the duct.
As the continuation, repeat the entrance duct flow TWSh execution for turbulent flow as set up in the model file. Perform the same analyses as specified for the laminar case. Do not attempt a beta =0 execution. 
Finally, a turbulent duct flow test is set up with conjugate heat transfer to the wall. Execute this case and, using Tecplot animation, observe the evolution of turbulent flow velocity and temperature solutions including within the wall. From sout, observe quasi-Newton convergence, the interplay between phi, sumphi, and pressure, and adherence to the constraints on y+ for the log-law BC. Appropriately interpret these solution data, documenting your conclusions on performance.  Prepare your report using the online template.
Due at class 24. 
 
8. Verify the GWSh, TWSh and FVSh algorithm template for 1-D linear unsteady convection-diffusion model problem. For pure 1-D convection of a smooth IC (gaussian, sine, etc), execute solutions for 0.25 <C<1.0 on uniform meshings, interpolating the IC onto 10 elements. Compare solution accuracy in eyeball and energy norms as function of Courant number, algorithm choice, and implicitness factor (theta). Ascertain the potential to affect phase error, hence accuracy via TWSh alpha, beta, and gamma terms, e.g., Raymond-Garder, Donea, least squares and theta not equal to 0.5. Repeat select executions for non-smooth square wave interpolated onto 2 elements. Prepare your report using the online template.
Due at class 28. 
 
9. Verify the GWSh-TWSh algorithm template for 1-D steady convection-diffusion. For the steady 1-D Peclet problem, confirm ES 551w experience with solution quality depending on non-uniform meshing for Pe=1000. Confirm solution monotonicity improvement using the optimal steady-state beta-term coupled with non-uniform mesh resolution for 103 < Pe < 104. Prepare your report using the online template.
Not assigned. 
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