Summary A 3D elasto‐plastic rate‐dependent model for rock mechanics is formulated and implemented into a Finite Element (FE) numerical code. The model is based on the approach proposed by Vermeer and Neher (A soft soil model that accounts for creep. In: Proceedings of the International Symposium “Beyond 2000 in Computational Geotechnics,” pages 249‐261, 1999). An original strain‐driven algorithm with an Inexact Newton iterative scheme is used to compute the state variables for a given strain increment.The model is validated against laboratory measurements, checked on a simplified test case, and used to simulate land subsidence due to groundwater and hydrocarbon production. The numerical results prove computationally effective and robust, thus allowing for the use of the model on real complex geological settings.

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.

No abstract

The numerical simulation of physical systems has become in recent years a fundamental tool to perform analyses and predictions in several application fields, spanning from industry to the academy. As far as large-scale simulations are concerned, one of the most computationally expensive tasks is the solution of linear systems of equations arising from the discretization of the partial differential equations governing physical processes. This work presents Chronos, a collection of linear algebra functions specifically designed for the solution of large, sparse linear systems on massively parallel computers. Its emphasis is on modern, effective, and scalable Algebraic Multigrid (AMG) preconditioners for high performance computing (HPC). This work describes the numerical algorithms and the main structures of this software suite, especially from an implementation standpoint. Several numerical results arising from practical mechanics and fluid dynamics applications with hundreds of millions of unknowns are addressed and compared with other state-of-the-art linear solvers, proving Chronos's efficiency and robustness.

No abstract

Summary Predicting the deformations of deep reservoirs due to fluid withdrawal/injection is a challenging task that could have important environmental, social, and economical impacts. Finite element models, if endowed with an appropriate constitutive law, represent a useful tool for computing the displacements, the deformations, and the stress distributions in reservoir applications. Several studies show that hypoelastic laws, based on a stress‐dependent vertical compressibility, are able to provide accurate results, confirmed by in situ and satellite measurements. On the other hand, such laws present some weaknesses related to the numerical implementation, in particular due to the nonsymmetry of the tangent operator. This paper presents a new constitutive model based on 2 invariants (the mean normal and deviatoric stresses), characterized by a variable pressure‐dependent bulk modulus K. This constitutive law allows for overcoming most shortcomings of the hypoelastic law, although preserving the same accuracy, reliability, and ease of use and calibration. This paper presents a procedure to identify the parameters of the new model, starting from the typically available data on the vertical compressibility. Numerical results show a good agreement between the 2 laws, suggesting the proposed approach as a valid alternative in reservoir applications.

Numerical modelling of geomechanical phenomena and geo-engineering problems often involves complex issues related to several variables and corresponding coupling effects. Under certain circumstances, both soil and rock may experience a non-linear material response, due to e.g. plastic, viscous or damage behavior, and even a nonlinear geometric one, due to large deformations/displacements of the solid. Furthermore, the presence of one or more fluids (water, oil, gas, etc.) within the skeleton must be accounted for when evaluating the interaction between the different phases of the continuum body. A multiphase three-dimensional coupled model in finite strains, suitable for dealing with solid-displacements/fluid-diffusion problems, is here described and an elasto-plastic behavior for the solid phase is assumed. Particularly, a 3D mixed finite element is implemented to fulfill stability requirements of the adopted formulation, as well as a permeability tensor dependent on deformation is introduced. A consolidation scenario induced by filling of silos is investigated and the effects of the adoption of finite strains discussed.

The numerical simulation of the physical systems has become in recent years a fundamental tool to perform analyses and predictions in several application fields, spanning from industry to the academy. As far as large scale simulations are concerned, one of the most computationally expensive task is the solution of linear systems arising from the discretization of the partial differential equations governing the physical processes. This work presents Chronos, a collection of linear algebra functions specifically designed for the solution of large, sparse linear systems on massively parallel computers (https://www.m3eweb.it/chronos/). Its emphasis is on modern, effective and scalable AMG preconditioners for High Performance Computing (HPC). This work describes the numerical algorithms and the main structures of this software suite, especially from the implementation standpoint. Several numerical results arising from practical mechanics and fluid dynamics applications with hundreds of millions of unknowns are addressed and compared with other state-of-the-art linear solvers, proving Chronos efficiency and robustness.