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Summary: This paper develops the scaled boundary finite element formulation for applications in coupled field problems, in particular, to poroelasticity. The salient feature of this formulation is that it can be applied over arbitrary polygons and/or quadtree decomposition, which is widely employed to traverse between small and large scales. Moreover, the formulation can treat singularities of any order. Within this framework, 2 sets of semianalytical, scaled boundary shape functions are used to interpolate the displacement and the pore fluid pressure. These shape functions are obtained from the solution of vector and scalar Laplacian, respectively, which are then used to discretise the unknown field variables similar to that of the finite element method. The resulting system of equations are similar in form as that obtained using standard procedures such as the finite element method and, hence, solved using the standard procedures. The formulation is validated using several numerical benchmarks to demonstrate its accuracy and convergence properties. [ABSTRACT FROM AUTHOR]

Summary: A methodology for the calculation of gradients with respect to design parameters in general fluid‐structure interaction problems is presented. It is based on fixed‐point iterations on the adjoint variables of the coupled system using algorithmic differentiation. This removes the need for the construction of the analytic Jacobian for the coupled physical problem, which is the usual limitation for the computation of adjoints in most realistic applications. The formulation is shown to be amenable to partitioned solution methods for the adjoint equations. It also poses no restrictions to the nonlinear physics in either the fluid or structural field, other than the existence of a converged solution to the primal problem from which to compute the adjoints. We demonstrate the applicability of this procedure and the accuracy of the computed gradients on coupled problems involving viscous flows with geometrical and material nonlinearities in the structural domain. [ABSTRACT FROM AUTHOR]

This paper presents an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by finite element methods on anisotropic meshes in [ABSTRACT FROM AUTHOR]

This work develops variational principles for the coupled problem of standard and extended Cahn-Hilliardtype species diffusion in solids undergoing finite elastic deformations. It shows that the coupled problem of diffusion in deforming solids, accounting for phenomena like swelling, diffusion-induced stress generation and possible phase segregation caused by the diffusing species, is related to an intrinsic mixed variational principle. It determines the rates of deformation and concentration along with the chemical potential, where the latter plays the role of a mixed variable. The principle characterizes a canonically compact model structure, where the three governing equations involved, that is, the mechanical equilibrium condition, the mass balance for the species content and a microforce balance that determines the chemical potential, appear as the Euler equation of a variational statement. The existence of the variational principle underlines an inherent symmetry of the coupled deformation-diffusion problem. This can be exploited in the numerical implementation by the construction of time-discrete and space-discrete incremental potentials, which fully determine the update problems of typical time stepping procedures. The mixed variational principles provide the most fundamental approach to the monolithic finite element solution of the coupled deformation-diffusion problem based on low-order basis functions. They induce in a natural format the choice of symmetric solvers for Newton-type iterative updates, providing a speedup and reduction of data storage when compared with nonsymmetric implementations. This is a strong argument for the use of the developed variational principles in the computational design of deformation-diffusion problems. [ABSTRACT FROM AUTHOR]

We consider weakly coupled LQ optimal control problems and derive estimates on the sensitivity of the optimal value function in dependence of the coupling strength. In order to improve these sensitivity estimates a 'coupling adapted' norm is proposed. Our main result is that if a weak coupling suffices to destabilize the closed loop system with the optimal feedback of the uncoupled system then the value function might change drastically with the coupling. As a consequence, it is not reasonable to expect that a weakly coupled system possesses a weakly coupled optimal value function. Also, for a known result on the connection of the separation operator and the stability radius a new and simpler proof is given. [ABSTRACT FROM AUTHOR]

SUMMARY Safety assessment of geosequestration of CO2 into deep saline aquifers requires a precise understanding of the study of hydro-chemo-mechanical couplings occurring in the rocks and the cement well. To this aim, a coupled chemo-poromechanical model has been developed and implemented into a research code well-suited to the resolution of fully coupled problems. This code is based on the finite volume methods. In a 1D axisymmetrical configuration, this study aims to simulate the chemo-poromechanical behaviour of a system composed by the cement well and the caprock during CO2 injection. Major chemical reactions of carbonation occurring into cement paste and rocks are considered in order to evaluate the consequences of the presence of CO2 on the amount of dissolved matrix and precipitated calcium carbonates. The dissolution of the solid matrix is taken into account through the use of a chemical porosity. Matrix leaching and carbonation lead, as expected, to important variations of porosity, permeability and to alterations of transport properties and mechanical stiffness. These results justify the importance of considering a coupled analysis accounting for the main chemical reactions. It is worth noting that the modelling framework proposed in the present study could be extended to model the chemo-poromechanical behaviour of the reservoir rock and the caprock when subjected to the presence of an acidic pore fluid (CO2-rich brine). Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Thermal recovery from a hot dry rock (HDR) reservoir viewed as a deformable fractured medium is investigated with a focus on the assumption of local thermal non-equilibrium (LTNE). Hydraulic diffusion, thermal diffusion, forced convection and deformation are considered in a two-phase framework, the solid phase being made by impermeable solid blocks separated by saturated fractures. The finite element approximation of the constitutive and field equations is formulated and applied to obtain the response of a generic HDR reservoir to circulation tests. A change of time profile of the outlet fluid temperature is observed as the fracture spacing increases, switching from a single-step pattern to a double-step pattern, a feature which is viewed as characteristic of established LTNE. A dimensionless number is proposed to delineate between local thermal equilibrium (LTE) and non-equilibrium. This number embodies local physical properties of the mixture, elements of the geometry of the reservoir and the production flow rate. All the above properties being fixed, the resulting fracture spacing threshold between LTNE and LTE is found to decrease with increasing porosity or fluid velocity. The thermally induced effective stress is tensile near the injection well, illustrating the thermal contraction of the rock, while the pressure contribution of the fracture fluid is negligible during the late period. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is well established that crop production is inherently vulnerable to variations in the weather and climate. More recently the influence of vegetation on the state of the atmosphere has been recognized. The seasonal growth of crops can influence the atmosphere and have local impacts on the weather, which in turn affects the rate of seasonal crop growth and development. Considering the coupled nature of the crop–climate system, and the fact that a significant proportion of land is devoted to the cultivation of crops, important interactions may be missed when studying crops and the climate system in isolation, particularly in the context of land use and climate change. To represent the two-way interactions between seasonal crop growth and atmospheric variability, we integrate a crop model developed specifically to operate at large spatial scales (General Large Area Model for annual crops) into the land surface component of a global climate model (GCM; HadAM3). In the new coupled crop–climate model, the simulated environment (atmosphere and soil states) influences growth and development of the crop, while simultaneously the temporal variations in crop leaf area and height across its growing season alter the characteristics of the land surface that are important determinants of surface fluxes of heat and moisture, as well as other aspects of the land-surface hydrological cycle. The coupled model realistically simulates the seasonal growth of a summer annual crop in response to the GCM's simulated weather and climate. The model also reproduces the observed relationship between seasonal rainfall and crop yield. The integration of a large-scale single crop model into a GCM, as described here, represents a first step towards the development of fully coupled crop and climate models. Future development priorities and challenges related to coupling crop and climate models are discussed. [ABSTRACT FROM AUTHOR]

In this paper, the length scales included both in rate-dependent single phase materials and in coupled problems such as saturated and partially saturated porous media where the viscous terms are introduced naturally by the fluid mass balance equations, are discussed. The viscous effects in the two problems are quite different and the internal length scales hence have different expressions. Also the wave speeds have different relationships with the wave number. [ABSTRACT FROM AUTHOR]

An implicit unconditionally stable partitioned solution procedure for the simultaneous integration of transient coupled field problems is presented. The procedure does not require that the full system of coupled equations be assembled, and allows use of existing single-field analysis software modules to solve the coupled field problem. An iterative partitioned conjugate gradient procedure is used to avoid having to form and assemble the Schur complement matrix. The coupling matrices never need be formed, thus resulting in substantial computational savings. © 1997 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Problems are structured when they are repetitive, routine, and well-defined. Standardized approaches including habit, tradition, standard operating procedures, and sophisticated analytical models are frequently used. Problems are ill-structured when they are novel, one of a kind, unfocused, and complex. Depending on the level in the organization in which the ill-structured problems occur, different problem-solving processes may be utilized. The Dewey and Dewey-Bentley models are proposed as general methodologies for solving operating problems at the lower levels of the organization. Simon's decision-process trichotomy is proposed as a methodology for solving strategic problems at the upper levels of the organization. Allison's three conceptual models are suggested as descriptive frameworks for understanding Simon's decision process. Based upon Allison's work, a normative model of strategic problem solving is developed. [ABSTRACT FROM AUTHOR]

Consider a mechanical system that contains slow and fast dynamics. Let it be possible, to split the potential energy into a slow and a fast potential and the configuration vector into slow and fast variables. For such systems, multirate schemes simulate the different parts using different time steps with the goal to save computing time. For the proposed multirate scheme, a time grid consisting of micro and macro nodes is used and the integrator is derived from a discrete variational principle. Variational integrators conserve properties like symplecticity and momentum maps and have good energy behavior. To solve the resulting system of coupled nonlinear equations, a Newton-Raphson iteration with an analytical Jacobian is used. It is demonstrated that the multirate approach leads to less computing time compared to singlerate simulation by means of three example systems, the Fermi-Pasta-Ulam problem, a triple spherical pendulum and a simple atomistic model, where the latter two are subject to constraints. Computing times are compared for different numbers of micro and macro nodes for dynamic simulations during a certain time interval. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]