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首页> 外文期刊>Journal of Computational Physics >Iterative multiscale finite-volume method
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Iterative multiscale finite-volume method

机译：迭代多尺度有限体积法

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The multiscale finite-volume (MSFV) method for the solution of elliptic problems is extended to an efficient iterative algorithm that converges to the fine-scale numerical solution. The localization errors in the MSFV method are systematically reduced by updating the local boundary conditions with global information. This iterative multiscale finite-volume (i-MSFV) method allows the conservative reconstruction of the velocity field after any iteration, and the MSFV method is recovered, if the velocity field is reconstructed after the first iteration. Both the i-MSFV and the MSFV methods lead to substantial computational savings, where an approximate but locally conservative solution of an elliptic problem is required. In contrast to the MSFV method, the i-MSFV method allows a systematic reduction of the error in the multiscale approximation. Line relaxation in each direction is used as an efficient smoother at each iteration. This smoother is essential to obtain convergence in complex, highly anisotropic, heterogeneous domains. Numerical convergence of the method is verified for different test cases ranging from a standard Poisson equation to highly heterogeneous, anisotropic elliptic problems. Finally, to demonstrate the efficiency of the method for multiphase transport in porous media, it is shown that it is sufficient to apply the iterative smoothing procedure for the improvement of the localization assumptions only infrequently, i.e. not every time step. This result is crucial, since it shows that the overall efficiency of the i-MSFV algorithm is comparable with the original MSFV method. At the same time, the solutions are significantly improved, especially for very challenging cases. (C) 2008 Elsevier Inc. All rights reserved.
机译：用于求解椭圆问题的多尺度有限体积（MSFV）方法已扩展为一种有效的迭代算法，该算法收敛于精细尺度数值解。通过使用全局信息更新局部边界条件，系统地减少了MSFV方法中的局部化误差。此迭代多尺度有限体积（i-MSFV）方法允许在任何迭代后保守重建速度场，并且如果在第一次迭代后重建速度场，则可以恢复MSFV方法。 i-MSFV方法和MSFV方法都可以节省大量计算量，因此需要椭圆问题的近似但局部保守的解决方案。与MSFV方法相比，i-MSFV方法可以系统地减少多尺度近似中的误差。每个方向上的线松弛都可以用作每次迭代的有效平滑器。此平滑器对于在复杂，高度各向异性的异构域中获得收敛至关重要。从标准的泊松方程到高度异质的各向异性椭圆问题，该方法的数值收敛已在不同的测试案例中得到验证。最后，为了证明在多孔介质中进行多相传输的方法的效率，表明仅偶尔（即不是每个时间步）应用迭代平滑程序来改善定位假设就足够了。该结果至关重要，因为它表明i-MSFV算法的总体效率与原始MSFV方法相当。同时，解决方案得到了显着改善，特别是对于非常具有挑战性的情况。 （C）2008 Elsevier Inc.保留所有权利。

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