Diffusion Discretization Method Properties

All three methods:

• Are cell-centered - balance equations are done over a cell
• Require cell-centered and face-centered unknowns to rigorously treat material discontinuities
• Preserve the homogeneous linear solution, and are second-order accurate
• Reduce to the standard cell-centered operator for an orthogonal mesh
• Maintain local energy conservation
• Morel-Hall Asymmetric Method
  • Described in

    Michael L. Hall, and Jim E. Morel. A Second-Order Cell-Centered Diffusion Differencing Scheme for Unstructured Hexahedral Lagrangian Meshes. In Proceedings of the 1996 Nuclear Explosives Code Developers Conference (NECDC), UCRL-MI-124790, pages 359-375, San Diego, CA, October 21-25 1996. LA-UR-97-8.

    which is an extension of

    J. E. Morel, J. E. Dendy, Jr., Michael L. Hall, and Stephen W. White. A Cell-Centered Lagrangian-Mesh Diffusion Differencing Scheme. Journal of Computational Physics, 103(2):286-299, December 1992.

    to 3-D unstructured meshes, with an alternate derivation.
• Hall Symmetric Method:
  • Based on the above method, but only applicable in 2-D x-y.
• Support Operator Symmetric Method:
  • Extension of the method described in

    Mikhail Shashkov and Stanly Steinberg. Solving Diffusion Equations with Rough Coefficients in Rough Grids. Journal of Computational Physics, 129:383-405, 1996.

    to 3-D unstructured meshes, with an alternate derivation.