Algorithms to solve nonlinear time-dependent problems of engineering and physics. Final report, 1 August 1986-31 May 1989
During this last year Osher developed a joint project with James Sethian concerning fronts propagating with curvature dependent speed. They devised new algorithms approximating the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand sides, by using techniques from hyperbolic conservation laws. Essentially non-oscillatory schemes are used. These methods accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, and work in any number of space dimensions. The methods can also be used for more general Hamilton-Jacobi type problems. Applications of the algorithms include crystal growth, solidification of metals and flame propagation.
- Research Organization:
- California Univ., Los Angeles, CA (USA). Dept. of Mathematics
- OSTI ID:
- 6717045
- Report Number(s):
- AD-A-221463/3/XAB
- Country of Publication:
- United States
- Language:
- English
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ALGORITHMS
CONSERVATION LAWS
CRYSTAL GROWTH
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
ELEMENTS
EQUATIONS
EQUATIONS OF MOTION
FLAME PROPAGATION
HAMILTON-JACOBI EQUATIONS
MATHEMATICAL LOGIC
METALS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE TRANSFORMATIONS
PHYSICS
PROGRESS REPORT
SOLIDIFICATION
TIME DEPENDENCE
VELOCITY