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System of Navier-Stokes equations in vector form

  Starting from this section we will consider all the problems in two dimensions only. For better-arranged description, let us rewrite governing equations (crossref 3) in (two-dimensional) vector form:

246(21.16)

where: 245 denotes the vector of unknowns (conservative quantities), 247 are the vectors of inviscid (convective) fluxes, 248 are the vectors of viscous (diffuse) fluxes, 243 is an additional matrix, that will be discussed.

Before using artificial compressibility method let us consider the vectors in the above equation have the following meaning:

243239244(21.17)
245 1239249(21.18)
250239251(21.19)
252239253(21.20)
254239255(21.21)
256239257(21.22)