Using wavelets to solve the Burgers equation: A comparative study
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801 (United States)
The Burgers equation is solved for Reynolds numbers [approx lt]8000 in a representation using coarse-scale scaling functions and a subset of the wavelets at finer scales of resolution. Situations are studied in which the solution develops a shocklike discontinuity. Extra wavelets are kept for several levels of higher resolution in the neighborhood of this discontinuity. Algorithms are presented for the calculation of matrix elements of first- and second-derivative operators and a useful product operation in this truncated wavelet basis. The time evolution of the system is followed using an implicit time-stepping computer code. An adaptive algorithm is presented which allows the code to follow a moving shock front in a system with periodic boundary conditions.
- OSTI ID:
- 6934808
- Journal Information:
- Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 46:12; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
MATHEMATICAL LOGIC
MECHANICS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
REYNOLDS NUMBER
WAVE PROPAGATION