Non-iterative adaptive time-stepping scheme with temporal truncation error control for simulating variable-density flow
Non-iterative adaptive time-stepping scheme with temporal truncation error control for simulating variable-density flow
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DOI：
10.1016/j.advwatres.2012.07.021
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发表时间：
2012-12
影响因子：
4.7
通讯作者：
E. Hirthe;T. Graf
中科院分区：
文献类型：
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作者：
E. Hirthe;T. Graf
Kavetski等人提出的基于时间截断误差的自动非迭代二阶时间步进方案[j]。具有自适应截断误差控制的非迭代时间步进Richards方程解。水资源资源2002；38(10):1211, http://dx.doi.org/10.1029/2001WR000720.]被实现到HydroGeoSphere模型的代码中。本文首次将该时间步进格式应用于多孔介质中自由对流的低瑞利数热Elder问题[van Reeuwijk M， Mathias SA, Simmons CT, Ward JD]。用伪光谱方法研究埃尔德问题。水资源资源2009；45:W04416, http://dx.doi.org/10.1029/2008WR007421.]，和solal [Shikaze SG， Sudicky EA, Schwartz FW]。离散裂缝地质介质中依赖密度的溶质输运：预测是否可行？J hydrogeology and engineering geology; 2000；[34:273-91]裂隙多孔介质中的自由对流问题。数值仿真结果表明，该方法通过控制时间步长，有效地将时间截断误差限制在用户定义的容差范围内。非迭代二阶时间步进格式可以应用于(i)热和溶质变密度流动问题，（ii）线性和非线性密度函数，以及（iii）包括多孔和裂缝-多孔介质在内的问题。
The automatic non-iterative second-order time-stepping scheme based on the temporal truncation error proposed by Kavetski et al. [Kavetski D, Binning P, Sloan SW. Non-iterative time-stepping schemes with adaptive truncation error control for the solution of Richards equation. Water Resour Res 2002;38(10):1211, http://dx.doi.org/10.1029/2001WR000720.] is implemented into the code of the HydroGeoSphere model. This time-stepping scheme is applied for the first time to the low-Rayleigh-number thermal Elder problem of free convection in porous media [van Reeuwijk M, Mathias SA, Simmons CT, Ward JD. Insights from a pseudospectral approach to the Elder problem. Water Resour Res 2009;45:W04416, http://dx.doi.org/10.1029/2008WR007421.], and to the solutal [Shikaze SG, Sudicky EA, Schwartz FW. Density-dependent solute transport in discretely-fractured geological media: is prediction possible? J Contam Hydrol 1998;34:273–91] problem of free convection in fractured-porous media. Numerical simulations demonstrate that the proposed scheme efficiently limits the temporal truncation error to a user-defined tolerance by controlling the time-step size. The non-iterative second-order time-stepping scheme can be applied to (i) thermal and solutal variable-density flow problems, (ii) linear and non-linear density functions, and (iii) problems including porous and fractured-porous media.