154
6. Methods for Unsteady Problems
both methods, but the error level is in this case determined by its initial
value.
Fig. 6.4. Isotherms in the unsteady 2D problem a t times t = 0.2 (upper left),
t = 0.5 (upper right), t = 1.0 (lower left) and t = 2.0 (lower right), calculated on a
uniform 20 x 20 CV grid using the CDS for spatial and the Crank-Nicolson method
for temporal discretization
We next examine the 2D test case of Chap. 4, which involves heat transfer
from a wall with prescribed temperature, exposed to a stagnation point flow,
see Sect. 4.7. The initial solution is again
= 0; the boundary conditions
do not change with time and are the same as in the steady state problem
investigated in Sect. 4.7, with p = 1.2 and r = 0.1. Spatial discretization is
by CDS, and a uniform grid with 20 x 20 CV is used. Linear equation systems
in case of implicit schemes are solved using SIP solver, and the convergence
error was reduced below lop5. We compute the time evolution of solution
towards the steady state. Figure 6.4 shows isotherms at four time instants.
In order to investigate the accuracy of the various schemes in this case,
we look at the heat flux through the isothermal wall at time t = 0.12. The
variation of the heat flux, Q, as a function of the time step size is shown