1549301742-The_Theory_of_Difference_Schemes__Samarskii

Conservative difference schemes of nonstationary gas dynarnics 527

a) The adiabatic flow of the ideal gas when w = 0, that is, x = 0.

Because of this, equations of gas dyna1nics (1), (6), (4) for the adia-

batic flow of the ideal gas can be represented by

(9)

av fJp

at - fJs ,

(10)

which will be put together with equation (8)

(11)

Thus, the resultant syste1n of equations con1prises l equations with respect

to four unknowns v, p, p and E.

We will use below the volume 17 = 1/ p instead of density p. In such a

setting the preceding equations can be represented by

(12)

(13)

817

at

av

fJs ,

p17=(1-l)E.

Equation (10) capable of describing the tootal energy can be replaced by

one of the newly formed equations

(14)

OE av

at = -p as ,

OE 01/

( 15) at = -p at ·

'

Indeed, taking into account the first equation (9) and (12), we obtain

o v^2 o OE ov op ov

(^0) = ot ( E + 2) + o s (p v) = ot + ( v ot + v o s) + P o s
OE ov OE 017
= ot + P os = 8t + P ot ·
b) The isotermic flow of the ideal gas when the temperature of gas
T = const and the equation of energy is missing. The condition T = const