2,238 research outputs found

    Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems

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    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 k≥1k\geq 1 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

    Well-posedness of the fully coupled quasi-static thermo-poro-elastic equations with nonlinear convective transport

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    This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists of a momentum balance equation, a mass balance equation, and an energy balance equation, fully coupled and nonlinear due to a convective transport term in the energy balance equation. The aim of this article is to investigate, in the context of mixed formulations, the existence and uniqueness of a weak solution to this model problem. The primary variables in these formulations are the fluid pressure, temperature and elastic displacement as well as the Darcy flux, heat flux and total stress. The well-posedness of a linearized formulation is addressed first through the use of a Galerkin method and suitable a priori estimates. This is used next to study the well-posedness of an iterative solution procedure for the full nonlinear problem. A convergence proof for this algorithm is then inferred by a contraction of successive difference functions of the iterates using suitable norms.Comment: 22 page

    On the Participation of Power-To-Heat Assets in Frequency Regulation Markets—A Danish Case Study

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    Due to the new green energy policies, district heating companies are being increasingly encouraged to exploit power-to-heat assets, e.g., heat pumps and electric boilers, in their distribution networks besides the traditional central combined heat and power units. The increased utilization of these assets will generate a more complex interaction between power distribution grids and district heating networks including markets for provision of ancillary services. Enabling the participation of power-to-heat units in the ancillary service markets, e.g., frequency reserves, may increase the revenue streams for assets’ owners. However, some technical challenges must first be addressed, including optimization of portfolios of assets that accounts for ancillary service markets, new coordination and operational schemes for portfolio of assets, increase data exchange and interactions with transmission system operators, and new local control schemes for units. This paper proposes a systematic model based design approach for assessment of provision of frequency regulation by power-to-heat assets using the smart grid architecture model. The proposed approach is demonstrated in a Real-Time Control Hardware-in-the-Loop laboratory environment

    The Fixed-Stress splitting scheme for Biot's equations as a modified Richardson iteration: Implications for optimal convergence

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    The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanics subproblems while adding a stabilizing term to the flow equation, which includes a parameter that can be chosen freely. However, the convergence properties of the scheme depend significantly on this parameter and choosing it carelessly might lead to a very slow, or even diverging, method. In this paper, we present a way to exploit the matrix structure arising from discretizing the equations in the regime of impermeable porous media in order to obtain a priori knowledge of the optimal choice of this tuning/stabilization parameter.acceptedVersio
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