孔隙弹性非线性Biot模型的参数鲁棒解耦离散化方法

IF 3.4 2区 数学 Q1 MATHEMATICS, APPLIED
Linshuang He , Xi Li , Minfu Feng
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引用次数: 0

摘要

针对具有位移相关非线性渗透率的Biot模型,提出了一种新的鲁棒解耦方案。该方案结合了低阶H(div)符合元对P1⊕RT0−P1近似和一阶半显式时间离散。在改进的类构象公式中加入两个稳定化项,以实现方案的稳定性。一项惩罚H(div)-符合分量的不一致性,另一项稳定压力振荡。所构造的方案依次求解位移和压力,使非线性项自然线性化,无需额外的内部迭代,从而提高了计算效率。改进了弱耦合条件,并在此条件下证明了在空间和时间上的最优收敛性。同时,我们的方案提供了鲁棒的解决方案,当lam系数趋于无穷大时,不会受到体积锁定的影响,当约束比存储系数和渗透率或时间步长趋于零时,不会出现虚假的压力振荡。最后,我们用几个非线性位移-渗透率关系的数值例子验证了这些理论结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A parameter-robust and decoupled discretization scheme for nonlinear Biot’s model in poroelasticity
We present a new robust and decoupled scheme for Biot’s model with displacement-dependent nonlinear permeability. The scheme combines a low-order H(div)-conforming element pair P1RT0P1 approximation with a first-order semi-explicit time discretization. Two stabilization terms are incorporated into the modified conforming-like formulation to achieve the scheme’s stability. One term penalizes the nonconformity of the H(div)-conforming component, and the other stabilizes pressure oscillations. The constructed scheme sequentially solves the displacement and pressure, which naturally linearizes the nonlinear terms without additional internal iterations, thus enhancing the computational efficiency. We improve the weak coupling condition and then prove optimal convergence in space and time under this condition. Meanwhile, our scheme provides robust solutions that do not suffer from volumetric locking as the Lamé coefficient tends to infinity and spurious pressure oscillations as the constrained specific storage coefficient and the permeability or time step go to zero. Finally, we verify these theoretical results with several numerical examples of nonlinear displacement–permeability relationships.
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来源期刊
Communications in Nonlinear Science and Numerical Simulation
Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
6.80
自引率
7.70%
发文量
378
审稿时长
78 days
期刊介绍: The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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