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Temperature dependent viscosity and conductivity GFM Problem Setup

A temperature dependent viscosity and conductivity model with slip and noslip boundary conditions was tested in a non-rotated frame with the GFM boundary, using the Sutherland model for perfect (constant specific heat) nitrogen. Again, as in the constant viscosity and conductivity model, the Clawpack and WENO methods were compared. The main difference of this test is the significant increase of the diffusive effects behind the Mach stem and around the shear/mixing layer. The viscosity and conductivity increase close to linearly with temperature, and the highest temperatures are between the Mach stem and the shear/mixing layer (aka the slipline in inviscid theory).

SutherlandModel

New Parameters for Nitrogen:

$\theta_{wedge} = 36 degrees, \quad \mu_ref=1.663*10^{-5} Pa*sec, \quad k_{ref} = 0.0242 W/(m*K)$

$T_{ref} = 273 K, \quad s_{\mu} = 107 K, }\quad s_{k} = 150 K$

$\quad m = 0.0140067 kg/mol,\quad \gamma = 1.4, \quad M=4.5$

$\quad T_0=300 K, \quad p_0 = 2000 Pa, \quad t_{final}=3*10^{-5} sec$

For the following tests, the configurations were:
Clawpack: base level 170x140 cells with 3-4 more levels, (x,y)[(-.005,.08)(.0,.07)], max cfl 0.9
WENO-TCD: base level 340x320 cells with 4 more levels refined 2,2,2,2 times respectively, (x,y)[(-.005,.08)(.0,.08)], max cfl 0.85)

DoubleMachReflectionStudy

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