Geodesic
Numerical model of the two-phase medium weak compressible matrix and some geophysical applications
Dalʹnevostočnyj matematičeskij žurnal, Tome 7 (2007) no. 1, pp. 79-90.

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Since the Boussinesq approximation cannot be applicable to model accumulation of a liquid phase (fluid) within a matrix the numerical model of two-phase medium with weak compressible matrix has been developed. Because of weak compressibility there is a lot of computational difficulties to solve the system of equations by a numerical method with sufficient accuracy. Therefore it has been obtained an asymptotical solution including the Boussinesq approximation as zero-order one. The finite element technique combined with the modified project gradient method is applied to obtain numerical solution for zero-order and following approximations. This method has considerable advantages in accuracy, stability and speed of response in comparison with penalty method and modified Lagrange function method. There has been fulfilled numerical modeling of a fluid accumulation within compressible matrix affected by the upper boundary's relief and variation of the fluid flow's distribution on the lower boundary. The model shear strain field are shown to be different in comparison with Boussinesq approximation. Some features of shear strain distribution have been studied analytically. Several geophysical applications of these model results is presented. 
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V. V. Pack. Numerical model of the two-phase medium weak compressible matrix and some geophysical applications. Dalʹnevostočnyj matematičeskij žurnal, Tome 7 (2007) no. 1, pp. 79-90. http://geodesic.mathdoc.fr/item/DVMG_2007_7_1_a7/

[1] E. V. Artyushkov, Fizicheskaya tektonika, Nauka, M., 1993, 456 pp.

[2] V. L. Bezverkhnii, V. V. Pak, “Flyuidodinamika i tektogenez Zapadno-Tikhookeanskoi zony perekhoda”, Vestnik DVO RAN, 2003, no. 4, 132–140 | MR

[3] Yu. M. Danilin, “O minimizatsii funktsii v zadachakh s ogranicheniyami tipa ravenstv”, Kibernetika, 1971, no. 2, 88–95 | MR | Zbl

[4] V. B. Zanemonets, V. D. Kotelkin, V. P. Myasnikov, “O dinamike litosfernykh dvizhenii”, Izv. AN SSSR. Fiz. Zemli, 1974, no. 5, 43–54

[5] A. V. Karakin, “Modeli flyuidodinamiki zemnoi kory s neuprugim skeletom”, Izv. AN SSSR, Fizika Zemli, 1990, no. 2, 3–15 | MR

[6] A. V. Karakin, L. I. Lobkovskii, “Gidrodinamika i struktura dvukhfaznoi astenosfery”, Dokl. AN SSSR, 268:2 (1983), 324–329

[7] A. V. Kiryukhin, V. M. Sugrobov, Modeli teploperenosa v gidrotermalnykh sistemakh Kamchatki, Nauka, M., 1987, 149 pp.

[8] G. I. Marchuk, Metody vychislitelnoi matematiki, Nauka, Novosibirsk, 1978, 536 pp. | MR

[9] R. I. Nigmatullin, Dinamika mnogofaznykh sred, v. 1, Nauka, M., 1987, 464 pp. | Zbl

[10] V. V. Pak, “Priblizhennyi metod rascheta medlennykh techenii neodnorodnoi vyazkoi neszhimaemoi zhidkosti”, Matematicheskoe modelirovanie i vychislitelnyi eksperiment, Voprosy vychisl. i prikl. matematiki, 85, RISO AN UzSSR, Tashkent, 1988, 11–22

[11] V. V. Pak, V. L. Bezverkhnii, K. G. Kuptsov, E. V. Beloliptseva, “Evolyutsiya teplovogo polya i filtratsiya flyuidov v aktivnykh zonakh perekhoda ot kontinenta k okeanu (chislennoe modelirovanie)”, V sb. “Informatika v okeanologii”, 1996, 38–47

[12] I. D. Ryabchikov, “Flyuidy v mantii Zemli”, Priroda, 1988, no. 13, 12–16

[13] R. Temam, Uravneniya Nave – Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981, 408 pp. | MR | Zbl

[14] D. Terkot, Dzh. Shubert, Geodinamika, v. 2, Geologicheskoe prilozhenie fiziki sploshnykh sred, Mir, M., 1985, 360 pp.

[15] V. P. Trubitsyn, E. V. Kharybin, “Konvektivnaya neustoichivost rezhima sedimentatsii v mantii”, Izv. AN SSSR. Fizika Zemli, 1987, no. 8, 21–30

[16] Yu. V. Khachai, “Konvektivnaya ustoichivost szhimaemoi zhidkosti dlya plotnostnykh modelei verkhnei mantii Zemli”, Izv. AN SSSR. Fizika Zemli, 1987, no. 8, 36–40

[17] W. D. Woidt, “Finite element calculations applied to saltdome analysis”, Tectonophysics, 50:2 (1978), 369–386