Finite volume coupling strategies for the solution of a Biot consolidation model
Finite volume coupling strategies for the solution of a Biot consolidation model
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DOI：
10.1016/j.compgeo.2013.09.014
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发表时间：
2014
影响因子：
5.3
通讯作者：
Roza Asadi;B. Ataie‐Ashtiani;C. Simmons
中科院分区：
文献类型：
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作者：
Roza Asadi;B. Ataie‐Ashtiani;C. Simmons
本文采用有限体积 (FV) 数值方法来求解具有不连续系数的 Biot 固结模型。我们的研究表明，FV 方案导致了一种局部质量保守的方法，该方法消除了压力振荡，特别是沿着具有不同属性的材料之间的界面，并产生了更高的流动和力学参数精度。然后利用这种数值离散来研究具有不同耦合程度的不同顺序策略，包括：迭代、显式和松散耦合方法。对所有这些顺序方法的稳定性、准确性和收敛速度进行了全面的研究。在迭代和显式解决方案中，研究了排水、不排水、固定应力和固定应变的四种分裂。在松耦合方法中，考虑了局部误差法、孔隙压力法和恒定步长这三种技术，并将结果与其他类型的耦合方法进行了比较。结果表明，与其他顺序方法相比，固定应力方法因其无条件稳定性、准确性和收敛速度而成为最佳算子分割。在松散耦合方案中，分别基于压力和位移变化的孔隙压力和局部误差方法显示出与问题的物理性质的一致性。在这些总机械迭代次数较少的方法中，可以实现可接受范围内的误差。由于在孔隙压力法中，力学时间步长增加得更加均匀，因此与局部误差法相比，该方法的成本更低。这些结果可能对解决方案选择的决策有用。此外，通过数值算例验证了FV方法在多层介质中的稳定性。
In this paper a finite volume (FV) numerical method is implemented to solve a Biot consolidation model with discontinuous coefficients. Our studies show that the FV scheme leads to a locally mass conservative approach which removes pressure oscillations especially along the interface between materials with different properties and yields higher accuracy for the flow and mechanics parameters. Then this numerical discretization is utilized to investigate different sequential strategies with various degrees of coupling including: iteratively, explicitly and loosely coupled methods. A comprehensive study is performed on the stability, accuracy and rate of convergence of all of these sequential methods. In the iterative and explicit solutions four splits of drained, undrained, fixed-stress and fixed-strain are studied. In loosely coupled methods three techniques of the local error method, the pore pressure method, and constant step size are considered and results are compared with other types of coupling methods. It is shown that the fixed-stress method is the best operator split in comparison with other sequential methods because of its unconditional stability, accuracy and the rate of convergence. Among loosely coupled schemes, the pore pressure and local error methods which are, respectively, based on variation of pressure and displacement, show consistency with the physics of the problem. In these methods with low number of total mechanical iterations, errors within acceptance range can be achieved. As in the pore pressure method mechanics time step increases more uniformly, this method would be less costly in comparison with the local error method. These results are likely to be useful in decision making regarding choice of solution schemes. Moreover, the stability of the FV method in multilayered media is verified using a numerical example.