Suppose you are interested in the steady state temperature profile T(x, y) of a square surface with
Question:
Suppose you are interested in the steady state temperature profile T(x, y) of a square surface with a known spatially dependent thermal diffusivity α(x, y) subject to Dirichlet boundary conditions. The time-dependent PDE governing this system is
and the boundary conditions are given by Fig. 7.16.
(a) List the most efficient combination of methods discussed in this book that you should use to solve the steady problem. In addition, using scaling arguments, estimate the time it would take to solve the problem with nx = ny = 100 nodes. Assume that if you discretize the x-domain using nx = 10 nodes and the y-domain using ny = 10 nodes, you get a program that runs in 10−1 seconds.
(b) Suppose the unsteady problem must reach a time t = 10 in order to reach equilibrium. List the combination of methods you would use to solve the unsteady problem. If one time step requires 10 ms, estimate the minimum number of seconds it will take to reach the steady state using a stable, explicit time integration method. Assume that max(λi) = 102, max[α(x, y)] = 1 and that the discretization is nx = ny = 101.
Step by Step Answer:
Numerical Methods With Chemical Engineering Applications
ISBN: 9781107135116
1st Edition
Authors: Kevin D. Dorfman, Prodromos Daoutidis