A new monolithic Newton‐multigrid‐based FEM solution scheme for large strain dynamic poroelasticity problems
A new monolithic Newton‐multigrid‐based FEM solution scheme for large strain dynamic poroelasticity problems
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DOI：
10.1002/nme.5315
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发表时间：
2017-02
影响因子：
2.9
通讯作者：
A. Obaid;S. Turek;Y. Heider;Bernd Markert
中科院分区：
文献类型：
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作者：
A. Obaid;S. Turek;Y. Heider;Bernd Markert
本文提出了一种新的有效的整体有限元解决方案来处理一组偏微分方程的二维，两相，饱和的多孔介质模型的理论与内在耦合和不可压缩的固体和流体成分的无限小和大的弹性变形。该方法继承了计算流体力学的一些技术，具有以下几个特点：（1）只进行算子计算，不需要额外的Gateaux导数。特别是，这里不涉及耗时的材料切线矩阵的计算;（2）它解决了非线性动力学问题，对耦合强度没有限制;（3）它比以前的工作中讨论的线性uvp求解器更有效;（4）它需要更弱的导数，因此可以测试低阶有限元;（5）边界条件得到简化，与解无关，比原UVP公式更便于应用。为了验证和比较的目的，进行了原型模拟，包括解析解，并在最后，一个自适应的时间步长程序被引入到处理的非线性迭代次数可能发生的快速变化。版权所有© 2016约翰威利父子有限公司.
This paper presents a new efficient monolithic finite element solution scheme to treat the set of PDEs governing a 2D, biphasic, saturated theory of porous media model with intrinsically coupled and incompressible solid and fluid constituents for infinitesimal and large elastic deformation. Our approach, which inherits some of its techniques from CFD, is characterized by the following aspects: (1) it only performs operator evaluation with no additional Gateaux derivatives. In particular, the computations of the time‐consuming material tangent matrix are not involved here; (2) it solves the non‐linear dynamic problem with no restriction on the strength of coupling; (3) it is more efficient than the linear uvp solver discussed in previous works; (4) it requires weaker derivatives, and hence, lower‐order FE can be tested; and (5) the boundary conditions are reduced, solution independent and more convenient to apply than in the old uvp formulation. For the purpose of validation and comparison, prototypical simulations including analytical solutions are carried out, and at the end, an adaptive time stepping procedure is introduced to handle the rapid change in the numbers of nonlinear iterations that may occur. Copyright © 2016 John Wiley & Sons, Ltd.