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Unformatted text preview: MAE 290B, Winter 2010 HOMEWORK 6 Due Wed 03-10-2010 in class Provide source codes used to solve all problems PROBLEM 1 Calculate the steady temperature distribution in a square plate (0 ≤ x < 2 π ,- π ≤ y < π ) that is kept at T ( x = 0 ,y ) = sin 2 ( y ) on one end and T ( x = 2 π,y ) = sin 4 ( y ) on its other end. Consider periodic boundary conditions in the vertical direction. The ratio k/ρc p is equal to unity, where k is the thermal conductivity of the plate, c p is its specific heat ratio and ρ is its density. Use a relaxation method with Implicit Euler ADI and second-order centered finite differences. Use N = 64 grid points in each direction. PROBLEM 2 Integrate numerically the linear wave equation ∂ t u + c∂ x u = 0 , in the domain 0 ≤ x < 10 with homogeneous initial conditions and u ( x = 0 ,t ) = sin( At ) Solve using second-order centered finite difference schemes with N = 200 grid points, Δ t = . 01 and the following boundary conditions at the artificial exit:...
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- Spring '10
- Boundary value problem, Boundary conditions, Convective Boundary Conditions, second-order centered ﬁnite