Neutronics computational applications of symmetry algebras
Lie groups of point transformations and their corresponding symmetry algebras are determined for a general system of second order differential equations, special cases of which include the multigroup diffusion equations and the ''FLIP form'' of the P/sub L/ equations. It is shown how Lie symmetry algebras can be used to motivate, formulate and simplify double sweep algorithms for solving two-point boundary value problems that involve systems of second order differential equations. A matrix Riccati equation that appears in double sweep algorithms is solved exactly by regarding a set of first integrals of the second order system as a set of first order differential invariants of the group of point transformations that is admitted by the system. A second computational application of symmetry algebras is the determination of invariant difference schemes which are defined as difference schemes that admit the same groups of point transformations as those admitted by the differential equations that they simulate. Prolongations of symmetry algebra vector fields that are required to construct invariant difference equations are defined and found. Examples of invariant difference schemes are constructed from the basic difference equation invariance conditions and shown to be exact. 15 refs.
- Research Organization:
- Los Alamos National Lab., NM (USA)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6452010
- Report Number(s):
- LA-UR-89-439; CONF-890408-9; ON: DE89007760
- Resource Relation:
- Conference: Advances in nuclear engineering computation and radiation shielding, Santa Fe, NM, USA, 9 Apr 1989; Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
NEUTRON DIFFUSION EQUATION
ANALYTICAL SOLUTION
NEUTRON TRANSPORT
BOUNDARY-VALUE PROBLEMS
ALGORITHMS
DIFFERENTIAL EQUATIONS
GROUP THEORY
MATRICES
RICCATI EQUATION
EQUATIONS
MATHEMATICAL LOGIC
MATHEMATICS
NEUTRAL-PARTICLE TRANSPORT
RADIATION TRANSPORT
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990230 - Mathematics & Mathematical Models- (1987-1989)