NMM: Week 5 - Finite Differences: PDE's

will langford

cba

8.1 - 1D Wave Equation

Undamped... dt = 0.1, [left] u(0,N/2) = 10, [right] u(:,N/2) = 2*e^(-0.5*(n/20)^2)

With Damping... dt = 0.1, y = 0.05, [left] u(0,N/2) = 10, [right] u(:,N/2) = 2*e^(-0.5*(n/20)^2)

8.2 - Diffusion

Explicit diffusion, u(0,N/2) = 1, [left] dt = 0.01, [middle] dt = 0.05, [right] dt = 1

Implicit diffusion, u(0,N/2) = 1, [left] dt = 0.05, [middle] dt = 1, [right] dt = 2

8.3 - 2D ADI Diffusion

u(0,:) = random, alpha = 1

8.4 - 2D SOR of Laplace Equation

[left] alpha = 1.0, [middle] alpha = 1.93, [right] alpha = 2.0

Source:

• 1D Wave
• Diffusion - Explicit
• Diffusion - Implicit
• Diffusion - 2D ADI
• 2D SOR - Laplace

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