The exact solution of the Reimann problem
(These plots are for the nondimensional time t= 0.148.)
The exact solution of the Reimann problem exhibits five distinct regions:
- Region 1 - the low pressure region
- Region 2 - the region between the shock wave and the contact discontinuity
- Region 3 - the region between the contact discontinuity and the rarefaction wave
- Region R - the rarefaction wave
- Region 3 - the high pressure region
Note that all the flow variables are discontinuous across the shock wave, that the density
and energy are discontinuous across the contact discontinuity, and that the
derivativesof the flow variables are discontinuous at the edges of the rarefaction
wave.
A flow sensitivity along the comparison plane
Exact sensitivities for the Reimann problem
Approximate sensitivities for the Lax-Wendroff method
Approximate sensitivities for the Godunov method
Approximate sensitivities for the Roe method.
Approximate sensitivities for the Lax-Wendroff
method on the medium grid
Approximate sensitivities for the Lax-Wendroff method on the
coarse grid.
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