Geodesic
Three-dimensional generalization for W-modification of a Godunov method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1659-1672

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A high-accuracy modification of Godunov's method for three-dimensional unsteady ideal gas flows is proposed. For the linear advection equation, a fully three-dimensional second-order accurate monotone scheme is designed with corrections computed on a variable stencil whose orientation depends on the signs of the equation coefficients. For the linear scalar advection equation, the scheme is proved to possess the positive approximation property. The method is tested by computing the flow in a three-dimensional Ludwieg tube with a square cross section. 
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     author = {E. I. Vasilev and A. S. Demin},
     title = {Three-dimensional generalization for {W-modification} of {a~Godunov} method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1659--1672},
     publisher = {mathdoc},
     volume = {48},
     number = {9},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a10/}
}
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E. I. Vasilev; A. S. Demin. Three-dimensional generalization for W-modification of a Godunov method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1659-1672. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a10/