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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits
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Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

机译：流动与地质力学耦合顺序方法的稳定性和收敛性：固定应力和固定应变分裂

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摘要

We analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics, in which the flow problem is solved first. We employ the von Neumann and energy methods for linear and nonlinear problems, respectively. We consider two sequential methods with the generalized midpoint rule for t_(n+α). where a is the parameter of time discretization: namely, the fixed-strain and fixed-stress splits. The von Neumann method indicates that the fixed-strain split is only conditionally stable, and that its stability limit is a coupling strength less than unity if α≥0.5. On the other hand, the fixed-stress split is unconditionally stable when a α≥0.5, the amplification factors of the fixed-stress split are different from those of the undrained split and are identical to the fully coupled method. Unconditional stability of the fixed-stress split is also obtained from the energy method for poroelastoplasticity. We show that the fixed-stress split is contractive and B-stable when α≥0.5. We also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward Euler method in time. From the estimates, the fixed-strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable. The fixed-stress split, however, is convergent for a fixed number of iterations, showing better accuracy than the undrained split. Even when we cannot obtain the exact local bulk modulus (or exact rock compressibility) at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials, the fixed-stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus, such as the dimension-based estimation, by which the employed local bulk modulus is less stiff than the exact local bulk modulus. We provide numerical examples supporting all the estimates of stability and convergence for the fixed-strain and fixed-stress splits.
机译：我们分析了流动和岩土力学相继隐式方法的稳定性和收敛性，其中首先解决了流动问题。我们分别对线性和非线性问题采用冯·诺依曼和能量方法。我们考虑t_（n +α）具有广义中点法则的两种顺序方法。其中a是时间离散化的参数：即固定应变和固定应力分裂。冯·诺伊曼方法表明，固定应变分裂仅在条件上是稳定的，并且如果α≥0.5，则其稳定极限是耦合强度小于一。另一方面，当α≥0.5时，固定应力裂缝是无条件稳定的，固定应力裂缝的放大系数与不排水裂缝的放大系数不同，并且与完全耦合方法相同。固定应力裂缝的无条件稳定性也可以通过孔隙弹塑性的能量方法获得。我们表明，当α≥0.5时，固定应力分裂是收缩且B稳定的。我们还通过基于矩阵和后向Euler方法的频谱分析，及时估计了两种顺序方法的收敛行为。根据估计，固定应变拆分可能不会以固定的迭代次数收敛，尤其是在稳定性极限附近，即使它是稳定的。但是，固定应力拆分收敛了固定的迭代次数，显示出比不排水拆分更好的准确性。即使由于复杂的边界条件或材料的非线性而无法先验地在流动步骤中获得确切的局部体积模量（或精确的岩石可压缩性）时，固定应力分裂仍可以通过适当估计以下项来提供稳定性和收敛性。局部体积模量，例如基于尺寸的估计，通过该局部体积模量，所使用的局部体积模量的刚性不如确切的局部体积模量大。我们提供了数值示例，支持对固定应变和固定应力裂缝的稳定性和收敛性的所有估计。

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  • 来源
    《Computer Methods in Applied Mechanics and Engineering》 |2011年第16期|p.1591-1606|共16页
  • 作者

    J. Kim; HA Tchelepi; R. Juanes;

  • 作者单位

    Department of Energy Resources Engineering, Stanford University, Creen Earth Sciences Bldg., 367 Panama Street, Stanford, CA 94305, USA,Earth Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road 90R1116, Berkeley, CA 94720, USA;

    Department of Energy Resources Engineering, Stanford University, Creen Earth Sciences Bldg., 367 Panama Street, Stanford, CA 94305, USA;

    Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Bldg. 48-319, Cambridge, MA 02141, USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Poromechanics; Geomechanics; Operator splitting; Von Neumann method; B-stability; Convergence;

    机译：动力力学地质力学;操作员拆分;冯·诺依曼法B稳定性收敛;

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