ME 7310

Project 3 Elliptic PDEs Due: Mon., Nov. 22, 2010 at 6:00 pm

Suppose that it is required to obtain the steady-state temperature distribution on a two-dimensional rectangular plate. The governing PDE for this problem is: ∂2T ∂2T + =0 ∂x2 ∂y 2

(1)

The plate has dimensions of L = 0.01 m and h = 0.02 m in x and y directions, respectively. The temperature at the boundaries are specified as: T (0, y) = 0 ; T (x, h) = 0 ; T (x, 0) = T0 = 100 K ;

∂T (L, y) = 0 ∂x

(2)

Use a 5-point formula (second order accurate) finite-difference approximation along with second order accurate boundary conditions. Solve the resulting system of equations using: 1. PSOR 2. LSOR 3. ADI The analytical solution is: Ta (x, y) =

∞ X n=1

2T0

i h −nπy −nπh nπy nπx 2L L e 2L ) − e sin( (1 − cos(nπ)) e −nπh 2L nπ(1 − e L )

(3)

Discuss the following: 1. Plot the residual vs. number of iteration for each method. Use different relaxation factors for PSOR and LSOR. 2. What relaxation factor values make PSOR and LSOR methods to converge faster? 3. Compare the CPU times of these methods. 4. Compare the numerical results with the analytical solution (T (x, y) vs. x) at y = 0.005, 0.01, 0.015 m.

## Project 3 - GitHub

Discuss the following: 1. Plot the residual vs. number of iteration for each method. Use different relaxation factors for PSOR and LSOR. 2. What relaxation factor ...

#### Recommend Documents

Project 4.3 - Project Proposal - GitHub
Nov 5, 2013 - software will find the optimal meet time for all users. This component is similar to the ... enjoy each others company! Existing Approaches:.

Project 4 - GitHub
Project 4. Vorticity-Stream F\rnction Method. Due: Mon., Dec. 6, 2010 at 6:00 pm. Consider the incompressible laminar flow in the plane channel shown below.

QR Reader Java Project - GitHub
QR Reader Java Project. Date: 4 July ... Open eclipse and click on File -> import -> General -> Existing projects into workspace as shown in fig. 2. ... Similarly fix problem of JRE system library if in ... ProjectFlow.pdf show complete flow of proje

Brooklyn Community District 3 - GitHub
Transportation/Utility. Public/Institutional. Open Space. Parking. Vacant. Other. 6,911. 6,373. 194. 1,457. 245. 199. 32. 368. 39. 284. 822. 71. U tica. A v. Broadway ... Bedford-Stuyvesant, Stuyvesant Heights, Tompkins Park North. Top 3 pressing iss

Operating Systems Homework #3 - GitHub
May 14, 2015 - (Integer) Number indicating scheduling algorithm. 27 int policy;. 28. // Enum values for policy. 29 const short FCFS=0, SJF=1, PRIOR=2, RR=3;.

Manhattan Community District 3 - GitHub
E 14 St. EastRiver. MN 6. MN 2. MN 1. Manhattan Community District 3. Neighborhoods1: Chinatown, East Village, Lower East Side, NoHo, Two Bridges. LAND USE MAP. 164,407. 163,277. -1% ... ACCESS TO PARKS7 of residents live within.

Queens Community District 3 - GitHub
This metric from the Mayor's Office for Economic Opportunity accounts for NYC's high cost of housing, as well as other costs of living and anti-poverty benefits. Land Use Category. % Lot. Area. # Lots. Click here for a more detailed land use map of Q