|
ИСТИНА |
Войти в систему Регистрация |
ИСТИНА ЦЭМИ РАН |
||
Mathematical modeling of coupled hydro-geomechanical processes with changing properties of the medium under finite strains using highperformance computingтезисы доклада
- Авторы: Vershinin* Anatoly, Levin Vladimir, Eremeev Victor, Podladchikov Yury
- Сборник: Book of abstracts 15th World Congress on Computational Mechanics (WCCM-XV)
- Тезисы
- Год издания: 2022
- Издательство: International Center for Numerical Methods in Engineering
- Местоположение издательства: Spain
- Первая страница: 2057
- Последняя страница: 2057
- Аннотация: The presentation outlines an approach to solving coupled non-stationary problems ofmodelling hydro-geomechanical processes taking into account both physical(poroelastoplasticity) and geometrical (finite strains) nonlinearities. The consideredporoelastoplastic model generalizes classical Biot's model for a two-phase liquid-saturatedporoelastic medium. A distinctive feature of this model is the two-way coupling betweenmechanical processes occurring in a porous elastoplastic matrix and a saturating viscous fluid,which makes it possible to take into account both the effect of a change in the pore pressure of afluid on the stress-strain state of a porous matrix and vice versa – an effect of a change in theshape of the pore space (due to the accumulated elastoplastic finite strains) on the pore pressure ina fluid. and, as a consequence of Darcy's law, on the rate of fluid flow inside the porous mediumtaking into account dynamic variations of both porosity and permeability.To simulate the accumulation of elastoplastic deformations, the plastic flow theory with anon-associated plasticity law is used according to the Drucker-Prager model, which takes intoaccount volumetric plastic deformation. In addition, within the framework of the consideredporoelastoplasticity model, the nonlinear dependence of the model parameters (elastic moduli,Biot's modulus, permeability, etc.) on porosity, which, in turn, depends on the volumetricdeformation of the skeleton, is taken into account. Non-recoverable plastic part of porosityvariation is considered also in the suggested mathematical model.For the numerical solution of the problem Galerkin’s method and the isoparametricspectral element method are used to discretize the geometric model and equations in space oncurvilinear unstructured meshes of high order (orders up to the 15th were used for solving modelproblems). The software implementation of the developed algorithm is performed using theCUDA technology. The spectral element mesh is naturally mapped onto the GPU’s Grid, andaccordingly, each spectral element is mapped onto a streaming block, within which individualSEM nodes are processed by the corresponding threads. This approach makes it possible toefficiently use the capabilities of shared memory for caching data inside a spectral element, whichsignificantly increases the throughput of the parallel version of the algorithm.Results of a numerical solution of several model problems are presented: a problem of thedevelopment of zones of localization of elastoplastic deformation near a well drilled in a porousrock saturated with fluid, a problem of a pure shear loading under finite strains of a model with acircular stress concentrator in its centre. The change in porosity and permeability because of theaccumulation of finite plastic strains is analysed.The research was performed in Lomonosov Moscow State University and was financiallysupported by the Ministry of Education and Science of the Russian Federation as part of theprogram of the Moscow Center for Fundamental and Applied Mathematics under the agreement№075-15-2019-1621 and by the grant of the President of the Russian Federation for youngscientists - doctors of sciences MD-208.2021.1.1.
- Добавил в систему: Вершинин Анатолий Викторович