论文标题
在域分解方法中使用代数双表示在3D域中的Darcy流量
Use of algebraic dual representations in domain decomposition methods for Darcy flow in 3D domain
论文作者
论文摘要
在这项工作中，我们将代数双表示与darcy方程的域分解方法结合使用。我们定义了损坏的Sobolev空间及其有限的尺寸对应物。此外，定义了一个全局痕量空间，该空间连接破裂空间之间的解决方案。双重表示的使用导致较少的无限制表示速度差异，压力梯度项和跨子域的连续性约束。为了证明这一点，我们解决了两个测试用例：i）制造解决方案案例，ii）工业基准储层建模问题SPE10。结果表明，与连续的Galerkin公式相比，域分解方案虽然具有更多未知数，但需要更少的存储器和模拟时间。
In this work we use algebraic dual representations in conjunction with domain decomposition methods for Darcy equations. We define the broken Sobolev spaces and their finite dimensional counterparts. In addition, a global trace space is defined that connects the solution between the broken spaces. Use of dual representations results in a sparse metric free representation of the constraint on divergence of velocity, the pressure gradient term and on the continuity constraint across the sub domains. To demonstrate this, we solve two test cases: i) manufactured solution case, and ii) industrial benchmark reservoir modelling problem SPE10. The results demonstrate that the domain decomposition scheme, although with more unknowns, requires less memory and simulation time as compared to the continuous Galerkin formulation.
