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6. Methods for Unsteady Problems
Although we were dealing with simple unsteady problems which have
a smooth transition from the initial to the steady state, we see that first
order Euler schemes are very inaccurate. In both test cases the second order
schemes had errors more than two orders of magnitude lower than the Euler
schemes (whose errors were of the order of 1% with the smallest time step).
One can expect that in transient flows even larger discrepancies can occur.
Of the first order schemes only the implicit Euler method can be used when
steady solutions are sought; for transient flow problems, second (or higher)
order schemes are recommended.
An unsteady flow problem will be discussed in Sect. 8.11.