Problem Description

• Mesh:
  • Kershaw, $\left\{\vphantom{ r,z }\right.$r, z$\left.\vphantom{ r,z }\right\}$ Mesh over 1 cm x 1 cm area
  • Grid size - 51 x 51 = 2601 nodes, 2500 cells
• Physics:
  • Two temperature, P₁ run
  • No removal or sources
  • Initial temperature of $\sqrt[4]{{10^5}}$ = 0.05623413 keV
• Boundary Conditions:
  • Black-body source at 1 keV at z = 0 cm
  • Vacuum boundary condition at z = 1 cm
  • Reflective boundaries at r = 0 cm and r = 1 cm
• Physical Constants:
  • No scattering
  • Absorption, emission and total cross sections defined via $\sigma$ = 30  T_mat^-3 cm^-1
  • Specific heat corresponds to an ideal gas with a density of 3 g/cc and $\overline{{a}}$ = 1 , giving a value of C_v = 0.4310461 jerks/cm³ /keV
• Opacity Evaluation:
  • Node opacities = Average of neighbor faces
  • Face opacities evaluated at average of cell center temperatures
  • Vacuum boundary face opacity equal to cell center opacity
  • Black-body source boundary face opacity evaluated at source temperature
• Solution Methods:
  • Morel Asymmetric Method, Support Operator Method
  • UMFPACK solver - an incomplete direct method
  • Time step limited so that the norm of the relative changes of T_mat , T_r , and $\phi$ are kept less than 0.03
  • Temperature floor set to 0.056 keV