Assignment Problem:
Consider a steady state two dimensional seepage problem as shown above. There are four different kinds of the boundary conditions in this problem. The pressure value is prescribed on Γ1, and Γ2; PΓ1 = 100 kPa, PΓ2 = 150 kPa. Γ3 is an impermeable surface, i.e. the flux in the normal direction to the surface is zero. Γ4 is a partially permeable so that the flux to the surface is given by J = 1 x 10-4 e m/s
The hydraulic conductivity of the porous medium is k = 4.2 x 10-6 m/s.
The governing equation of this problem is given by a Laplace equation, i.e.
2P = ∂2P/∂x2 + ∂2P/∂y2 = 0
Subjected to
P = P0 on Γ0 (Dirichlet condition)
-k∂P/∂n = Jn on ΓJ (Neumann condition)
Q1. Investigate the problem and build a plan for the numerical analysis.
Q2. Build the solution procedure.
Q3. Solve the system and consider to the following questions.
- Provide the pressure field.
- Calculate the amount of water passing throughout Γ* in an hour. (Approximate the thickness = 1m)
- Provide the field of the maximum flux, i.e.
Jx = -k.∂P/∂x, Jy = -k.∂P/∂y
J = √(Jx2 + Jy2)
Q4. Discuss your result.
Use your own linear algebraic solver.
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