The Pencil Code

Results from tests

samples/1d-tests

• 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).

  no B-field	with B-field	shock with B-field
  cf. Fig. 1 of Falle (2002)	cf. Fig. 2 of Falle (2002)	cf. Fig. 6 of Falle (2002)

• 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.
  ν=0.05, χ=0.0002.
• 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.
  ν=χ=η=0.07.
• 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.
  ν=χ=η=2.
• 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.