Consider the numerical solution to the 2-d steady state diffusion equation in the unit square with boundary conditions of 0 on all surfaces except at x=0. = 0 C = 1,x = 0 C= 0, x = 1,y = 0,1 a) Show that by central difference discretization that the concentration at the ij position is the simple average of the concentrations surrounding that point. b) Discretize the equation with Ax=Ay=0.33. If 0 and 3 represent the i, j indices on the known boundaries, the unknown points are C1,C12, C21, C22. Write the equations to be solved for these 4 unknowns in matrix form.

Consider the numerical solution to the 2-d steady state diffusion equation in the unit square with boundary conditions of 0 on all surfaces except at x=0. = 0 C = 1,x = 0 C= 0, x = 1,y = 0,1 a) Show that by central difference discretization that the concentration at the ij position is the simple average of the concentrations surrounding that point. b) Discretize the equation with Ax=Ay=0.33. If 0 and 3 represent the i, j indices on the known boundaries, the unknown points are C1,C12, C21, C22. Write the equations to be solved for these 4 unknowns in matrix form.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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