G‘OVAK ANIZOTROP MUHITTA SIRT TO‘LQINLARINING TARQALISHI VA UNING MATEMATIK MODELLARI
DOI:
https://doi.org/10.47390/ts-v3i10y2025No7Ключевые слова:
g‘ovak-elastiklik, Biot modeli, anizotropiya, Rayleigh to‘lqini, Love to‘lqini, dispersiya, so‘nish, SBP SAT, HDG, teskari masala.Аннотация
Ushbu maqolada g‘ovak anizotrop muhitda sirt to‘lqinlarining tarqalishini modellashtirish uchun matematik fizik asos va barqaror sonli yondashuvlar taklif etiladi. Biot nazariyasining to‘liq anizotrop shaklidan boshlab, o‘lchov aralash formulirovka uchun energiya barqaror, simmetrik zaif shakl hosil qilinadi. Erkin sirt va qatlamlararo interfeyslar uchun SAT (yaqinlashtiruvchi qo‘shimcha hadlar) - barqarorlashtirish mexanizmi tavsiya etiladi. SBP–SAT (qismlarga ajratib yig‘ish va bir vaqtning o‘zida yaqinlashtiruvchi hadlar) - yuqori tartibli chekli farqlar va HDG (Gibridlashtiriladigan uzlukli Galerkin usuli) usullariga tayangan diskretizatsiyalar ishlab chiqilib, mos energiya bahosi va kuzatuvli dispersiya xatoliklari keltiriladi. Bezarazmerlash orqali boshqaruvchi guruhlar (filtratsion viskozlik, Biot moduli, samarali kuchlanish koeffitsienti, dinamik tortuozlik, anizotropiya darajasi) aniqlanib, TI (transvers izotrop) yarim cheksiz muhit uchun sekulyar tenglama va Rayleigh faza tezligining Fréchet sezgirlik integral operatorlari olinadi. Sonli tajribalar azimutiy dispersiya, permeabilitet va sirt shartlarining (drenajlangan/drenajlanmagan) kuchli ta’sirini ko‘rsatadi. Yondashuv seysmika, geotexnika va kollektor monitoringi muammolari uchun amaliy ahamiyatga ega.
Библиографические ссылки
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