123 research outputs found
A study on iterative methods for solving Richards` equation
This work concerns linearization methods for efficiently solving the
Richards` equation,a degenerate elliptic-parabolic equation which models flow
in saturated/unsaturated porous media.The discretization of Richards` equation
is based on backward Euler in time and Galerkin finite el-ements in space. The
most valuable linearization schemes for Richards` equation, i.e. the
Newtonmethod, the Picard method, the Picard/Newton method and theLscheme are
presented and theirperformance is comparatively studied. The convergence, the
computational time and the conditionnumbers for the underlying linear systems
are recorded. The convergence of theLscheme is theo-retically proved and the
convergence of the other methods is discussed. A new scheme is
proposed,theLscheme/Newton method which is more robust and quadratically
convergent. The linearizationmethods are tested on illustrative numerical
examples
Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems
In this paper we develop adaptive iterative coupling schemes for the Biot
system modeling coupled poromechanics problems. We particularly consider the
space-time formulation of the fixed-stress iterative scheme, in which we first
solve the problem of flow over the whole space-time interval, then exploiting
the space-time information for solving the mechanics. Two common
discretizations of this algorithm are then introduced based on two coupled
mixed finite element methods in-space and the backward Euler scheme in-time.
Therefrom, adaptive fixed-stress algorithms are build on conforming
reconstructions of the pressure and displacement together with equilibrated
flux and stresses reconstructions. These ingredients are used to derive a
posteriori error estimates for the fixed-stress algorithms, distinguishing the
different error components, namely the spatial discretization, the temporal
discretization, and the fixed-stress iteration components. Precisely, at the
iteration of the adaptive algorithm, we prove that our estimate gives
a guaranteed and fully computable upper bound on the energy-type error
measuring the difference between the exact and approximate pressure and
displacement. These error components are efficiently used to design adaptive
asynchronous time-stepping and adaptive stopping criteria for the fixed-stress
algorithms. Numerical experiments illustrate the efficiency of our estimates
and the performance of the adaptive iterative coupling algorithms
Aspects regarding innovation management in services industry
Innovation is reshaping the corporate culture of organizations in this present age of competency and service legacy. Innovation in services is getting recognition from the top executives due to its strategic importance and globalizes competition, which has escalated the demand of better change and adoption of best practices through change in processes. Innovation has been studied in a variety of contexts, including in relation to technology, commerce, social systems, economic development, and policy construction. There are, therefore, naturally a wide range of approaches to conceptualizing innovation in the scholarly literature. This article attempts to contribute to this latter discussion and progress towards further clarification of the specific characteristics of services innovation, while also identifying common features.service innovation, innovation management, knowledge management
Towards hybrid two-phase modelling using linear domain decomposition
The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g., in soil layers in contact with the atmosphere) the system can be substituted by the scalar Richards model. Thus, the porous medium domain may be partitioned into disjoint subdomains where either the full two-phase or the simplified Richards model dynamics are valid. Extending the previously considered one-model situations we suggest coupling conditions for this hybrid model approach. Based on an Euler implicit discretization, a linear iterative (L-type) domain decomposition scheme is proposed, and proved to be convergent. The theoretical findings are verified by a comparative numerical study that in particular confirms the efficiency of the hybrid ansatz as compared to full two-phase model computations.publishedVersio
Iterative Coupling for Fully Dynamic Poroelasticity
We present an iterative coupling scheme for the numerical approximation of the mixed hyperbolic-parabolic system of fully dynamic poroelasticity. We prove its convergence in the Banach space setting for an abstract semi-discretization in time that allows the application of the family of diagonally implicit Runge–Kutta methods. Recasting the semi-discrete solution as the minimizer of a properly defined energy functional, the proof of convergence uses its alternating minimization. The scheme is closely related to the undrained split for the quasi-static Biot system.acceptedVersio
A linear domain decomposition method for partially saturated flow in porous media
The Richards equation is a nonlinear parabolic equation that is commonly used
for modelling saturated/unsaturated flow in porous media. We assume that the
medium occupies a bounded Lipschitz domain partitioned into two disjoint
subdomains separated by a fixed interface . This leads to two problems
defined on the subdomains which are coupled through conditions expressing flux
and pressure continuity at . After an Euler implicit discretisation of
the resulting nonlinear subproblems a linear iterative (-type) domain
decomposition scheme is proposed. The convergence of the scheme is proved
rigorously. In the last part we present numerical results that are in line with
the theoretical finding, in particular the unconditional convergence of the
scheme. We further compare the scheme to other approaches not making use of a
domain decomposition. Namely, we compare to a Newton and a Picard scheme. We
show that the proposed scheme is more stable than the Newton scheme while
remaining comparable in computational time, even if no parallelisation is being
adopted. Finally we present a parametric study that can be used to optimize the
proposed scheme.Comment: 34 pages, 13 figures, 7 table
Composite slab behavior and strength analysis under static and dynamic loads
Steel-framed buildings are typically constructed using steel-deck-reinforced concrete floor slabs. The in-plane (or diaphragm) strength and stiffness of the floor system are frequently utilized in the lateral load-resisting system design. This paper presents the results of an experimental research program in which four full size composite diaphragms were vertically loaded to the limit state, under static or dynamic loads. Two test specimens were provided with longitudinal steel-deck ribs, and the other two specimens with cross steel-deck ribs. Typical composite diaphragm limit states are described, and the controlling limit state for each of the full size tests is indicated. The interaction effects between the reinforced concrete slab and the steel girder on the composite slab strength and stiffness were mainly studied
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