Construction of Difference Equations Using Lie Groups
The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Office of Defense Program (US)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 1172
- Report Number(s):
- LA-13499; TRN: US0101269
- Resource Relation:
- Other Information: PBD: 1 Aug 1998
- Country of Publication:
- United States
- Language:
- English
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