Problem Experience (PE) sets are transmitted as PDF file e-mail attachments. Preparation instructions will be provided. The PE Archive containing select completed problems will be opened one class date following submittal date. All PE assignments are taken from the text unless otherwise stated. PE assignments submitted after the archive is opened will not be accepted.	Due
1.1	Solve the steady viscous laminar-thermal incompressible non-D Navier-Stokes PDE system for 2-D fully developed thermal flow between horizontal parallel plates.   Assume the fluid is water with BCs no-slip walls and plate fixed uniform temperatures T1 and T2 > T1.  Assume the viscous dissipation term in DE is negligible, then evaluate its magnitude using your computed NS solution.	4
2.0	Concepts, Terminology, Methodology:
.1	2.4.1 - 2.4.4
.2	2.5.1,  2.5.2	6
3.0	Weak Form Duality, Quadratic Forms, Galerkin optimality, Regular Mesh Refinement, Asymptotic Error Estimate:
.1	2.6.1 - 2.6.3
.2	2.7.1, 2.7.2
.3	2.8.1 - 2.8.3
.4	2.10.1, 2.10.2
.5	2.11.1 - 2.11.3
.6	3.4.1, 3.4.2, 3.5.1 - 3.5.3	8
4.0	Aerodynamics Weak Interaction Theory, Farfield Potential, Laminar Boundary Layer, Galerkin optimal Validation:
.1	4.2.1
.2	4.3.1, 4.3.2
.3	4.4.1 - 4.4.3
.4	4.5.1	10
5.0	Time Averaged NS, Turbulent Boundary Layer, Parabolic NS PDE Systems, Reynolds Stress Modeling:
.1	4.9.1, 4.9.2
.2	4.9.3 - 4.9.5
.3	4.10.1 - 4.10.4
.4	4.12.1, 4.12.3	14
6.0	NS PDE System, Well-Posed BCs, DM Issues, Vector Field Theory State Variables, modified Galerkin optimal Validation:
.1	5.2.1 - 5.2.4
.2	5.3.1
.3	6.2.1 - 6.2.3
.4	6.3.1, 6.3.2
.5	6.3.3, 6.3.4
.6	6.3.5
7.0	Pressure Projection State Variable NS, modified Galerkin optimal Validation, Space-Time Dispersion Error Annihilation, Time Averaged RaNS mPDE Validation:
.1	5.4.1 - 5.4.3
.2	7.2.1 - 7.2.2
.3	7.4.1, 7.4.3 - 7.4.5
.4	B.7.1 - B.7.4
.5	7.7.1, 7.7.2
.6	8.2.1, 8.2.2
.7	8.3.1 - 8.3.3 .	20
8.0	Free-Surface Hydrodynamics, Hyperbolic Conservation Law Forms, Tidal RaNS, Courseware pages referenced:
.1	Confirm depthordered DPz produces the third equation on page FSNS.1.
.2	Verify that DM is ill-posed as an ODE for vertical velocity, FSNS.2.
.3	Verify the turbulent depth-averaged hydrodynamics non-D PDE system, FSNS.5, then confirm hyperbolic conservation law form on FSNS.7.
.4	Verify hyperbolic conservation law GWSN to GWSh + TS algorithm flux vector jacobians, FSNS.9.
.5	Confirm accuracy of the non-D mGWSh + TS algorithm statement for depth-averaged hydrodynamic NS, FSNS.10-11.
.6	Repeat PE 8.5 replacing the TS-generated "beta" terms therein with optimal coefficient h2Fr/12.   Note appearance of Fr2.	26
9.0	Fourier Theory Spectral Analyses, modified Galerkin optimal Derivations:
.1	5.6.1 - 5.6.4
.2	5.6.5 - 5.6.9
.3	5.6.5, 5.6.6
.4	5.7.1 - 5.7.3
.5	5.9.1 - 5.9.5
.6	5.11.1 - 5.11.2
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