Geodesic
ENO and WENO versions of Bott's scheme for advection equation
Matematičeskoe modelirovanie, Tome 20 (2008) no. 10, pp. 86-98

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Consecutive generalization of the Bott's scheme for advection equation based on ENO and WENO techniques is suggested. Modified scheme inherits all good properties of original scheme (accuracy and positiveness) and prove to be non-oscillatory. Two variants of 3- and 5-points stencil for flux approximation are considered. WENO versions of these variants have 5-th and 9-th order of accuracy respectively for smooth solutions under constant advection velocity condition. It is shown that the use of coordinate splitting for multi-dimensional cases does not make worse order of accuracy comparing with one-dimensional one. 
@article{MM_2008_20_10_a7,
     author = {A. A. Ignatyev},
     title = {ENO and {WENO} versions of {Bott's} scheme for advection equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {86--98},
     publisher = {mathdoc},
     volume = {20},
     number = {10},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_10_a7/}
}
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A. A. Ignatyev. ENO and WENO versions of Bott's scheme for advection equation. Matematičeskoe modelirovanie, Tome 20 (2008) no. 10, pp. 86-98. http://geodesic.mathdoc.fr/item/MM_2008_20_10_a7/