519.63 + 532.529.5
DOI: 10.14529/^150210


.. 1, .. 2
1 - , . ;
2 , .
. , . , , . , . , . , .
: , , , , , .

, . , , , , , . , [1] . , , (, [2]). : , [3], , [4]. [1, 5] .
[6] [7] , . , , .
1.
(), [5]. [5] :
1,1^1 = 2 + 22 = 0 + 2 = _ ( )
' ' 0 (11)
= 1 (1, = 2{∞2, 2), = ([, 1), 2 = 2(2, 2) ,
\ = !1, = ∞22 , 1 + 2 = 1, = + = 1, 2) , (1.5)
/ = 21 (1 - 2)\1 - 2\/8, = - 2). (1.6)
(1.1)(1.6) : = 1(1 - 0) + 0, = (_1)^ , 2 = 2(2 - 0). (1.7)
1, 2 ; ∞, ^ ( = 1, 2) - ; , - , , -
, 7- ; - , - ; 1 2 - : 0 - : - ; R1 - ; - , () () : - ; ^ - .
(1.1) - ; (1.2) - ; (1.3) (1.4) - . (1.6) - , () (/) : (1.7) - . [8].
(1.2)-(1.4) .
1, 2, :
. -,2
V

:
^ 1^
+ -^ = - (18)
2~ 22^ -
+ = + (19) (1.3) (1.4) . (1.1) :
11 111 ± 1 ... ^ 1
1 + = + - ^ - (110)
22 222 2 2∞2 , .
+^ = ^)+. (111)
(1.1) :
1 , ^. 2∞ _ ∞ (2 , 22\
2~= 2\ + ~
(1.10) (1.11) , :
11 111 1 11^ ... ,, ^
1" + = + ~) + - ^ - > (112)
+ = - + (1.13)
^ \ ) ^ '
.., ..

(1.3) (1.4) , :
^ + +?-) + nf^v1-v2)-, (1.14)
+ = (15)
(1.8), (1.9), (1.14), (1.15).
(122) + [1ї11 + 222 + (11 + 22)] = 0. (1.16)
(1.1), (1.2), (1.5)-(1.7), (1.14)(1.16) , .
= 0,
=
-, 1 = (
7 = nq,
2.
[6] (1.1), (1.2), (1.5)(1.7), (1.14)(1.16) :
%=0. (2.1) lf' p^ = -aiirx + nf' (22)
+ a-^-) + nf(y1-v2)-nq, (2.3)
(2.4)
(1%2) + ^ + ^] = 0' (25)
(2 = const), (2.1), (2.3), (2.5) :
dPi ∞ 2 _ _ 1-^=0, 2 =0, -=0, Pl = ∞, (2.6)
Pi ^ = -(1 + 2 ^ + "/Oi - v2) - , (2.7)
1 + 2 , d(vlP) + ^ d(v2p) = 0 (?8)
(1.7) (2.7)
+ - *) - "") (2.9)
(2.9), + 1 i - 1/2 i + 1/2 i - 1, i i + 1:
+1
. (fc-l)
Pi+1/2 ; ( 1 ~a. (al,i + l/2^Vl,i + l Vl,i)
+ 2+1/2(^ + 1 - - ^(<1/2^1/2^ +
1,1+1/2
+ 2/^1/2(^+1/2 - ^2^1+1/2)(2.10)
"1,1+1/2
- , - . :
^-*, (2.11)
^ + /^ (2.12)
vl,i vm - Pi + 1/2
v2,i vm -V2,i Pi + 1/2
:
ffi/2 = (tfiT1 + )/2, *2"m/2 = (^1 + )/2. (2.13)

1 = + -^ (2.14)

_m ?+1 | _ +1 _ _ ? , _ -
Pl,iil,i + Pl,i 2,i = Pl,ihl,i + P2,t^2, -
^n fim+1 ~m+l n ftm+l ^m+l At
lal,i + l/2yl,i + l/2Pi + l/2 al,i-l/2Vl,i-l/2Pi-l/2j ^
(a2,i + l/2^2} + l/2Pi + l/2 a2,i-l/2^i-l/2Pi^l/2) ^ (215)
, .. .. [6].

1. ї [9] [10].
2. , (2.10)-(2.15) , [6] [11] ї [9] [10] .
. .
.
13 - 01 - 00072.

1. , .. / .. // - . - 2011. - . 84, 1. - . 74-92.
2. , .. /.. , .. // . - 1990. - . 312, 1. - . 50-54.
3. , .. / .. , .. // . ї. - 2014. - . 7, 3. - . 40-49.
4. , .. /.. , .. // . ї. - 2014. - . 7, 2. - . 29-37.
5. , .. / .. , .. // . , , ї. - 2014. - . 14, 1. - . 57-62.
6. , .. / .. , .. . - .: , 1982. - 392 .
7. , .. /.. // . - 2002. -. 14, 8. - . 51-55.
8. , .. / .. // . - 1984.- . 20, 2. - . 102-107.
9. , .. / .. , .. // . - 1988. - 1. - . 115-117.
.., ..

10. , .. /.. , .. //. - 1988. - 1. - . 51-57.
11. , .. / .. , .. // . - 1983. - . 14, 6. - . 47-60.
, - .-. , , , - , . ; yum_kov@mail.ru.
, . .-. , , , . ; ea_kov@mail.ru.
18 2015 .
DOI: 10.14529/ctcr150210
METHOD OF LARGE PARTICLES FOR RESEARCH OF CURRENTS OF GAS-SUSPENSIONS
Yu.M. Kovalev, South Ural State University, Chelyabinsk, Russian Federation, yum_kov@mail.ru, E.A. Kovaleva, Chelyabinsk State University, Chelyabinsk, Russian Federation, ea_kov@mail.ru
Modification of a method of large particles in the annex to researches of currents of gas-suspensions was developed. It is shown that this modification of method of large particles allows to carry out calculations of behavior of shock waves in gas-suspensions without introduction in an explicit form of artificial viscosity. It allowed to eliminate distortions of a physical picture of a current of the gas-suspension connected with existence of the ostsillyation taking place at distribution of shock waves in non-uniform environments. It was shown that the obvious option of modification of a method of large particles when using of the offered modification for carrying out calculations of distribution of shock waves in gas-suspensions with large numbers of Courant can be used. It allows to reduce considerably time of calculation of a task and to avoid carrying out the difficult iterative procedures inherent in implicit differential schemes. It is shown that the offered modification is effective and allows to carry out calculations of shock waves in gas-suspensions with large numbers of Courant.
Keywords: numerical method, mathematical model, gas-suspensions, conservation laws, shock waves, number of Courant.
References
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Received 18 March 2015

, .. / .. , .. // . , , ї. -2015. - . 15, 2. - . 91-96. 1: 10.14529/150210
REFERENCE TO ARTICLE
Kovalev Yu.M., Kovaleva E.A. Method of Large Particles for Research of Currents of Gas-Suspensions. Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control, Radio Electronics, 2015, vol. 15, no. 2, pp. 91-96. (in Russ.) DOI: 10.14529/ctcr150210