Partial Differential Equations

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Partial Differential Equations

QUESTION 2

2.1 Assume you have a 2D concrete slab that has dimensions of 1 x 1. The boundaries x=0

and y=0 both have a temperature of 00C, while the boundaries x=1 and y=1 both have a

temperature of 150x and 120y respectively.

(i) Plot/draw the computational domain taking step sizes in both the x-direction and

the y-direction to be 0.1 units. Show all the boundary conditions. (10)

(ii) How many computational nodes are in this problem? (5)

2.2 Assuming the problem is a steady state heat distribution problem, write the

mathematical equation that can represent this phenomena.

2.3 Use the forward finite difference approximation method to solve this problem. Express

your answer as a matrix only. (20)

QUESTION 3

If the problem in Q2 has the boundary along y=0 as a Neumann boundary. Solve the

problem using the forward finite difference approximation, and present your answer as a

matrix. (20)

QUESTION 4

If the corner of the boundary along x=0 and y=0 in Q2 is curved, show how the nonuniform

spacing in the curved boundary can be accounted for. (15)

Civil-Engineering

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