Mathematical Theory of Compressible Viscous Fluids by Eduard Feireisl Trygve G. Karper & Milan Pokorný

Author:Eduard Feireisl, Trygve G. Karper & Milan Pokorný
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(7.7)

or a more subtle variant

(7.8)

The expression

is called upwind in numerical analysis.

The “dissipative part” in the upwind (7.8) is active only if , while its counterpart can be seen as a finite volume approximation of the artificial viscosity term − h α Δ r. In this book, we use a modified upwind formula that can be seen as a compromise between (7.7) and (7.8), namely

(7.9)

which can be equivalently written as

(7.10)

where we have chosen (Fig. 7.6)

(7.11)

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