Finding nonoscillatory solutions to difference schemes for the advection equation

The advection equation is solved using a weighted adaptive scheme that combines a monotone scheme with the central-difference approximation of the first spatial derivative. The determination of antidiffusion fluxes is treated as an optimization problem. The solvability of the optimization problem is...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2008-09, Vol.48 (9), p.1646-1657
Main Author: Kivva, S. L.
Format: Article
Language:English
Subjects:
Advection
Algorithms
Approximation
Computational mathematics
Computational Mathematics and Numerical Analysis
Cost analysis
Fluxes
Lagrange multiplier
Linear programming
Mathematics
Mathematics and Statistics
Nonlinear programming
Optimization
Studies
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Summary:The advection equation is solved using a weighted adaptive scheme that combines a monotone scheme with the central-difference approximation of the first spatial derivative. The determination of antidiffusion fluxes is treated as an optimization problem. The solvability of the optimization problem is analyzed, and the differential properties of the cost functional are examined. It is shown that the determination of antidiffusion fluxes is reduced to a linear programming problem in the case of an explicit scheme and to a nonlinear programming problem or a sequence of linear programming problems in the case of an implicit scheme. A simplified monotonization algorithm is proposed. Numerical results are presented.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542508090133