A Domain Decomposition Approach for Local Mesh Refinement in Space and Time
A Domain Decomposition Approach for Local Mesh Refinement in Space and Time
复制标题
时空局部网格细化的域分解方法
DOI：
10.2118/191703-ms
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
M. Wheeler
中科院分区：
文献类型：
--
作者：
Gurpreet Singh;M. Wheeler
复杂多相流和输运问题的储层模拟经常遭受非线性求解器收敛问题。这些表现在限制性的小的时间步长的形式，即使使用无条件稳定的全隐式计划。当使用局部网格细化来精确地表示可用的储层参数（诸如渗透率、孔隙度等）时，这些问题进一步复杂化。在多个空间尺度上。我们讨论了一种区域分解方法，该方法允许在储层的不同子域（Singh和惠勒（2018））中进行不同的时间步长和网格细化，从而在不影响计算效率和预测精度的情况下规避这些问题。该方法将空间中的局部网格细化的公知方法（惠勒等人（2002））扩展到时间。我们的数值实验表明，非线性求解器无法收敛到所需的公差，由于在一个较小的子域大的非线性残差。我们利用这一功能，以确定子域中较小的时间步长是必要的，而使用大的时间步长在其余的水库域。我们的方法的三个关键组成部分是：（1）时空、增强速度、区域分解方法，其允许不同子域中的不同网格细化和时间步长，同时保持局部质量守恒，（2）基于残差的误差估计器，以识别或标记区域（或子域），造成非线性收敛问题，和（3）一个完全耦合的单片求解器也提出了解决粗和精细子域问题，在空间和时间上同时进行该方案是完全隐式的，因此是无条件稳定的。结果表明，使用大的时间步长为整个水库域造成严重的非线性求解器收敛问题。虽然对整个域使用较小的时间步长可以减少收敛问题，但也会导致大量的计算开销。所提出的空间-时间域分解方法，具有较小的时间步长在一个子域和大的时间步长在其他地方，避免了非线性收敛问题，而不增加计算成本。此外，时空整体求解器呈现出大规模并行，时间并发框架，用于解决地下多孔介质中的流动和运输问题。由于所提出的方法是类似于广泛使用的有限差分格式，它可以很容易地集成到任何现有的传统油藏模拟器。
Reservoir simulations for complex multiphase flow and transport problems often suffer from non-linear solver convergence issues. These manifest in the form of restrictively small time-step sizes even while using unconditionally stable fully implicit schemes. These problems are further compounded when a local mesh refinement is used to accurately represent reservoir parameters available such as permeability, porosity, etc., at multiple spatial scales. We discuss a domain decomposition approach that allows different time-step sizes and mesh refinements in different subdomains (Singh and Wheeler (2018)) of the reservoir that circumvents these issues without compromising computational efficiency and prediction accuracy. This approach extends the well-known methodology of local mesh refinement in space (Wheeler et al. (2002)) to time. Our numerical experiments indicate that non-linear solvers fail to converge, to the desired tolerance, due to large non-linear residuals in a smaller subdomain. We exploit this feature to identify subdomains where smaller time-step sizes are necessary while using large time-step sizes in the rest of the reservoir domain. The three key components of our approach are: (1) a space-time, enhanced velocity, domain decomposition approach that allows different mesh refinements and time-step sizes in different subdomains while preserving local mass conservation, (2) a residual based error estimator to identify or mark regions (or subdomains) that pose non-linear convergence issues, and (3) a fully coupled monolithic solver is also presented that solves the coarse and fine subdomain problems, both in space and time, simultaneously. This solution scheme is fully implicit and is therefore unconditionally stable. The results indicate that using large time-step sizes for the entire reservoir domain poses serious non-linear solver convergence issues. Although using a smaller time step size for the entire domain reduces the convergence issues, it also results in substantial computational overheads. The proposed space-time domain decomposition approach, with smaller time-step sizes in a subdomain and large time-step sizes everywhere else, circumvents the non-linear convergence issue without adding computational costs. Additionally, a space-time monolithic solver renders a massively parallel, time concurrent framework for solving flow and transport problems in subsurface porous media. Since the proposed approach is similar to the widely used finite difference scheme, it can be easily integrated in any existing legacy reservoir simulator.
日本儿童和学生对 TIMSS 科学论文式任务的反应特征 (7) - 9 项任务分析结果的趋势 -
DOI：
--
发表时间：
2005
期刊：
日本科学教育学会年会論文集 第29号
影响因子：
--
作者：
中山 迅;大場裕子;猿田祐嗣
通讯作者：
猿田祐嗣