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Influence of Boundary Condition Types on Unstable Density-Dependent Flow

机译：边界条件类型对不稳定的依赖于密度的流的影响

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摘要

Boundary conditions are required to close the mathematical formulation of unstable density-dependent flow systems. Proper implementation of boundary conditions, for both flow and transport equations, in numerical simulation are critical. In this paper, numerical simulations using the FEFLOW model are employed to study the influence of the different boundary conditions for unstable density-dependent flow systems. A similar set up to the Elder problem is studied. It is well known that the numerical simulation results of the standard Elder problem are strongly dependent on spatial discretization. This work shows that for the cases where a solute mass flux boundary condition is employed instead of a specified concentration boundary condition at the solute source, the numerical simulation results do not vary between different convective solution modes (i.e., plume configurations) due to the spatial discretization. Also, the influence of various boundary condition types for nonsource boundaries was studied. It is shown that in addition to other factors such as spatial and temporal discretization, the forms of the solute transport equation such as divergent and convective forms as well as the type of boundary condition employed in the nonsource boundary conditions influence the convective solution mode in coarser meshes. On basis of the numerical experiments performed here, higher sensitivities regarding the numerical solution stability are observed for the Adams-Bashford/Backward Trapezoidal time integration approach in comparison to the Euler-Backward/Euler-Forward time marching approach. The results of this study emphasize the significant consequences of boundary condition choice in the numerical modeling of unstable density-dependent flow.
机译：需要边界条件以关闭不稳定的依赖于密度的流动系统的数学公式。在数值模拟中，对于流动和输运方程，边界条件的正确实现至关重要。在本文中，使用FEFLOW模型进行数值模拟，以研究不同边界条件对不稳定的依赖密度的流动系统的影响。研究了与Elder问题类似的设置。众所周知，标准Elder问题的数值模拟结果强烈依赖于空间离散化。这项工作表明，对于在溶质源处采用溶质质量通量边界条件而不是指定浓度边界条件的情况，由于空间的不同，对流求解模式（即羽状结构）的数值模拟结果不会发生变化。离散化。此外，研究了各种边界条件类型对非源边界的影响。结果表明，除了空间离散和时间离散等其他因素外，溶质运移方程的形式（例如发散和对流形式）以及非源边界条件中采用的边界条件的类型也会对​​对流求解模式产生较大的影响。网格。根据此处执行的数值实验，与Euler-Backward / Euler-Forward时间行进方法相比，Adams-Bashford / Backward梯形时间积分方法的数值解稳定性更高。这项研究的结果强调了边界条件选择在不稳定的依赖于密度的流动数值模拟中的重大后果。

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  • 来源
    《Ground water》 |2014年第3期|378-387|共10页
  • 作者

    Behzad Ataie-Ashtiani; Craig T. Simmons; Adrian D. Werner;

  • 作者单位

    National Centre for Groundwater Research & Training and School of the Environment, Flinders University, G.P.O. Box 2100, Adelaide, SA 5001, Australia;

    National Centre for Groundwater Research & Training and School of the Environment, Flinders University, G.P.O. Box 2100, Adelaide, SA 5001, Australia;

    National Centre for Groundwater Research & Training and School of the Environment, Flinders University, G.P.O. Box 2100, Adelaide, SA 5001, Australia;

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