On the solvability of incompressible Stokes with viscoplastic rheologies in geodynamics
On the solvability of incompressible Stokes with viscoplastic rheologies in geodynamics
复制标题
地球动力学中粘塑性流变不可压缩斯托克斯的可解性
DOI：
10.1002/2015gc006228
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发表时间：
2016
期刊：
影响因子：
3.7
通讯作者：
C. Wilson
中科院分区：
文献类型：
--
作者：
M. Spiegelman;D. May;C. Wilson
塑性/破坏是地球动力学模型中的一个重要组成部分，因为地球材料不能承受无限的应力。然而，许多问题仍然是适当的模型，以及有效的解决这些强非线性系统的塑性。在这里，我们提出了一些简化的模型问题，旨在阐明目前在地球动力学模拟中使用的粘塑性问题的描述和解决方案所涉及的许多问题。我们考虑了等粘层上粘塑性层的压缩和拉伸，并引入了一个单一的塑性屈服准则，其中包括最常用的粘塑性模型：von Mises，depth-dependent von Mises和Drucker-Prager。我们发现，对于所有考虑的流变学，连续的替代方案（又名皮卡迭代）往往停滞在大值的非线性残差，产生虚假的解决方案。然而，组合Picard-Newton格式对于与动压无关的流变学是有效的。当解决依赖于动态压力的流变学的不可压缩斯托克斯问题时，例如Drucker-Prager粘塑性，会出现困难。分析表明，当偏应力张量对动压的依赖性（即，|τ/|）变大。我们的经验表明，在这些情况下，牛顿解算器可以失败，引入虚假的剪切带，并讨论解释非收敛计算的结果的后果。即使对于求解器收敛的问题，Drucker-Prager粘塑性也可以产生明显偏离岩石静力学的动态压力，并且应该评估速度场和压力场以确定解决方案是否在地质上合理。
Plasticity/failure is an essential ingredient in geodynamics models as earth materials cannot sustain unbounded stresses. However, many questions remain as to appropriate models of plasticity as well as effective solvers for these strongly nonlinear systems. Here we present some simplified model problems designed to elucidate many of the issues involved for the description and solution of viscoplastic problems as currently used in geodynamic modeling. We consider compression and extension of a viscoplastic layer overlying an isoviscous layer and introduce a single plastic yield criterion which includes the most commonly used viscoplasticity models: von Mises, depth‐dependent von Mises, and Drucker‐Prager. We show that for all rheologies considered, successive substitution schemes (aka Picard iteration) often stall at large values of the nonlinear residual, producing spurious solutions. However, combined Picard‐Newton schemes can be effective for rheologies that are independent of the dynamic pressure. Difficulties arise when solving incompressible Stokes problems for rheologies that depend on the dynamic pressure such as Drucker‐Prager viscoplasticity. Analysis suggests that incompressible Stokes can become ill‐posed when the dependence of the deviatoric stress tensor on dynamic pressure (i.e., |∂τ/∂p′| ) becomes large. We demonstrate empirically that, in these cases, Newton solvers can fail by introducing spurious shear bands and discuss the consequence of interpreting the results of nonconverged computations. Even for problems where solvers converge, Drucker‐Prager viscoplasticity can produce dynamic pressures that deviate significantly from lithostatic and both the velocity and pressure fields should be evaluated to determine whether solutions are geologically reasonable.
Spud 1.0：科学计算机模型的用户界面的通用化和自动化
DOI：
10.5194/gmdd-1-125-2008
发表时间：
2008
期刊：
--
影响因子：
--
作者：
Ham D
通讯作者：
Ham D