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322 10. Inviscid Compressible Flow
Implicit CFL=0.5e e=0.1 Implicit CFL=0.9e e=0.1
Theory Theory
250 500 750 1000 1250 250 500 750 1000 1250
X X
Implicit CFL=2.0e e=0.1 Implicit CFL=5.0e e=0.1
Theory Theory
250 500 750 1000 1250 250 500 750 1000 1250
X X
Fig. 10.17. Shock tube model problem: gas states at time t — 250; CFL variation.
Another set of calculation was made, but this time the CFL number was kept
at 1.0 and the explicit artificial viscosity coefficients were varied from .0001 to
10. The numerical results are be compared with the theoretical values in Fig.
10.18. It can be seen that the dissipation errors increase with the values of e e,
and that the shock wave has almost merged with the expansion wave for the
case when e e — 10.
10.14 Model Problem for the Implicit Method:
Quasi-ID Nozzle
The model problem is the quasi-lD nozzle problem of Section 10.11 and the
initial conditions (subsection 10.11.1) and boundary conditions (subsection
10.11.2) are identical.
