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Assignments are noted on the ME422 calendar. Labs employ provided, and are to be completed by the class indicated. The script files below employ the fempse1.4 toolbox in conjunction with Matlab. Be sure to install Matlab from tibia and have your path point to your installed location of the fempse1.4 toolbox. Limit narrative to a single page with tabular data and plots appended as appropriate. Archival verification data and extensive lab reports are available to registered students at http://www.rose-hulman.edu/ME422/Private/Archives_labs/index.shtml Student reports can be accessed from http://www.rose-hulman.edu/ME422/student_labs.shtml Notify instructor of completion by e-mail. Late labs will not be accepted. |
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| lab | lab assignment |
| L-00 |
Prepare your on-line reporting environment (see minimalist example) in your personal Rose-Hulman web area. Make it spiffy! Due at Class 7. |
| L-01 |
Using the Lab01 matlab script for steady-state one-dimensional conduction and a four element discretization: (1) present the assembled GWSh via LHS Q = RHS before and after modification for Dirichlet data, (2) present a plot of the four element temperature distribution. Then perform a uniform mesh refinement until the left temperature has converged to within 0.01, reporting both TL and Enorm and a plot of the converged temperature distribution. Due at Class 11. |
| L-02 |
Using the Lab02 matlab script for steady-state one-dimensional conduction with no source and boundary convection, perform a mesh convergence study for linear, quadratic, and cubic element bases. Starting with a two element discretization, uniformly refine the mesh 6 times. Verify the asymptotic error estimate using the energy semi-norm and in TL, presenting appropriate tables and graphs. Due at Class 14. |
| L-03 |
Using the Lab03 matlab script as a starting point, fill in the required code to solve the simply supported beam with a uniform distributed load of w(x)=100 lb/ft in the downward direction. Use the two variable formulation to obtain nodal values of moment and deflection and then post-process to obtain the nodal values of shear and slope from their definitions Perform a uniform mesh refinement study for the linear basis only in enorm of moment and deflection until round-off error is clearly evident. From your convergence study, identify the mesh for your most accurate solution and present a shear / moment / slope / deflection graph for this mesh. Due at Class 21. |
| L-04 |
Using the jacobian and residual developed for problem P-06a, solve for the temperature distribution using a 32 element grid and a thermal conductivity of k(t) = 73.2 - 0.04T - 0.000003T2 Verify and report quadratic convergence for the iterative solver. Then remove one term from the jacobian, resolve, and comment on solution convergence/divergence. Due at Class 24. |
| L-05 |
Using the Lab05 matlab script as a starting point, fill in the details for transient heat conduction with an x-dependent source of s(x)=0.1*sin((x/L)*pi). For the 32 element grid and Theta=0.5, start with a time step size of 100 seconds and uniformly refine it until the midpoint solution to converges to 1e-4 at the final time of tf=2000 seconds. Repeat for both Theta=0 and Theta=1.0. Then present a plot of the tfsolution for each value of Theta for a time step of 12.5 seconds, commenting on the accuracy of each solution. Finally, report and discuss temporal convergence rates in Enorm at the final time for each value of Theta. Due at Class 28. |
| L-06 |
Using the Lab06 matlab script as a starting point, fill in the details for the Peclet problem. For Theta=1, an initial mesh of 4 elements, a non-dimensional final time of 1000, and a timestep size of 100, find and present the uniform mesh required for visually accurate steady solutions to Pe = 0.1,1,10, and 100. Comment on the behavior of the numerical solution for each value of Peclet. Knowing the required mesh for a spatially accurate solution at each Pe, set Theta=0.5 and find the required time step size for a monotone transient evolution for each Pe. Note: do not try to find the timestep required for theta=0 - it is very small! Finally, for the monotone and accurate solution to Pe=100, generate a profile report and report the percentage of time spent constructing [JAC] and {FQ} versus the percentage of time spent solving the matrix statement via PINV. Bonus: employ ratlist to generate a non-uniform spatial and temporal discretization to obtain a monotone and accurate solution to Pe=100. Due at Class 31. |
| L-07 |
Using the given boundary conditions for the Burger's Equation, create the code to solve steady shock problem. Without knowing the exact solution for the transient evolution and the steady state, obtain a solution which is monotone and accurate in time and space using the user-controlled parameters of mesh refinement (uniform or non-uniform), timestep size, artificial dissipation, and a value of Theta. Be sure to discuss your selection of parameters and show some kind of convergence in your solution. Repeat for the traveling shock problem. Due at the Final Exam. |
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Prof. Zac Chambers Last modified: |