Sod shock tube tests (checked in under samples/1d-tests/sod_10
to sod_1000). Initial condition is a smoothed (width=0.03) isothermal
pressure jump ranging from 10:1 to 1000:1.
pressure jump 10:1
pressure jump 100:1
pressure jump 1000:1
ν=.02, χ=.0005, t=2.7:
ν=.04, χ=.0005, t=1.9:
ν=.08, χ=.0005, t=1.5:
The values of viscosity are chosen rather conservatively;
for weak shocks one can get away with less viscosity
(ν=.014 for 10:1 and
ν=.028 for 100:1).
For strong shocks (pressure jumps of 1000:1 and above) the
discrepancy compared with the inviscid analytic solution
becomes quite noticeable.
Rarefaction shocks (checked in under samples/1d-tests/expans, expans_bfield and riemann_bfield).
Conditions for non-magnetic rarefaction shock. Left state: ρ=1, p=10, ux=-3. Right state: ρ=.87469, p=8, ux=-2.46537.
This corresponds to s/cp=1.68805 on both sides. 800 points.
Conditions for magnetic rarefaction shock. Left state: ρ=1, p=.2327, ux=-4.6985, uy=-1.085146, Bx=-0.7, By=1.9680. Right state: ρ=.7270, p=.1368, ux=-4.0577, uy=-0.8349, Bx=-0.7, By=1.355.
This corresponds to s/cp=-0.5682 on both sides. 800 points.
Conditions for magnetic Riemann problem. Left state: ρ=0.5, p=10, ux=0, uy=2, Bx=2, By=2.5. Right state: ρ=0.1, p=0.1, ux=-10, uy=0, Bx=2, By=2.
This corresponds to s/cp=2.38119 on the left and 1.22753 on the right. 800 points.
Note: in the tests above, uniform viscosity is used. The
viscosity has to be chosen such as to cope with the strongest
compression in the domain. By using
a nonuniform (artificial)
viscosity, both compression and expansion shocks can be made as
sharp as possible.