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An adaptive multiscale approach for modeling two-phase flow in porous media including capillary pressure

機(jī)譯：一種用于建模包括毛細(xì)管壓力在內(nèi)的多孔介質(zhì)中兩相流的自適應(yīng)多尺度方法

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Many important applications in porous media require the large-scale simulation of complex physical processes. Due to the limitations of computational resources, huge model domains often have to be simulated on relatively coarse grids. However, depending on the application, a high spatial resolution may be necessary to capture important effects, for example due to small-scale heterogeneities. One solution strategy is multiscale modeling. The idea is to decrease the number of global degrees of freedom while preserving important fine-scale features. In this work, we present a multiscale approach for modeling two-phase flow in porous media, which is applicable in a wide range of flow regimes, but especially if the influence of capillary pressure is significant. In this case, many existing upscaling or multiscale techniques, originally developed and successfully used for advection-dominated systems, fail or are not able to yield sufficiently accurate results. We combine an adaptive grid method based on multipoint flux approximation with various local upscaling techniques. In particular, the numerical method has to be able to treat complex effective parameters like anisotropic phase permeabilities. A crucial point is the development of suitable grid-adaptation strategies to account correctly for important effects. The method is tested and proven to work for various examples including varying heterogeneous parameter fields and different flow regimes.
機(jī)譯：多孔介質(zhì)中的許多重要應(yīng)用都需要對復(fù)雜的物理過程進(jìn)行大規(guī)模模擬。由于計算資源的限制，通常必須在相對粗糙的網(wǎng)格上模擬巨大的模型域。然而，取決于應(yīng)用，例如由于小規(guī)模的異質(zhì)性，可能需要高的空間分辨率來捕獲重要的效果。一種解決方案策略是多尺度建模。這個想法是在保留重要的精細(xì)尺度特征的同時減少全局自由度的數(shù)量。在這項工作中，我們提出了一種用于多孔介質(zhì)中兩相流建模的多尺度方法，該方法適用于廣泛的流態(tài)，但是特別是在毛細(xì)管壓力的影響很大的情況下。在這種情況下，許多最初開發(fā)并成功用于對流占主導(dǎo)地位的系統(tǒng)的現(xiàn)有升級或多尺度技術(shù)都將失敗或無法產(chǎn)生足夠準(zhǔn)確的結(jié)果。我們將基于多點通量近似的自適應(yīng)網(wǎng)格方法與各種局部放大技術(shù)相結(jié)合。特別地，數(shù)值方法必須能夠處理復(fù)雜的有效參數(shù)，例如各向異性相的滲透率。關(guān)鍵點是開發(fā)適當(dāng)?shù)木W(wǎng)格自適應(yīng)策略以正確考慮重要影響。該方法經(jīng)過測試并證明可用于各種示例，包括變化的異構(gòu)參數(shù)字段和不同的流態(tài)。

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  • 來源
    《Water resources research》 |2013年第12期|8139-8159|共21頁
  • 作者

    M. Wolff; B. Flemisch; R. Helmig;

  • 作者單位

    Department of Hydromechanics and Modeling of Hydrosystems, University of Stuttgart, Pfaffenwaldring 61,DE-70569 Stuttgart, Germany;

    Department of Hydromechanics and Modeling of Hydrosystems, University of Stuttgart, Stuttgart, Germany;

    Department of Hydromechanics and Modeling of Hydrosystems, University of Stuttgart, Stuttgart, Germany;

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