Multiscale model reduction techniques for coupled flow and transport in porous media
Description: Transport processes in porous media cannot be separated from the flow. Indeed, the transport equation constitutes the material balance law for transported constituents. The transport equation is often convection-dominated and driven by a multiscale velocity field. Solving these multiscale transport equations can be very challenging computationally due to disparity of scales, high variations in the velocity field, and high Peclet number. Moreover, one also needs to resolve fine-scale features of the velocity field, which includes multiple scales and high contrast. Thus, developing reduced-order models, that are stable and accurate, is a challenging task in many applications including material sciences, filtration, membrane applications, groundwater hydrology, petroleum engineering, and so on. There are a number of traditional approaches, which include numerical homogenization, numerical upscaling, multiscale finite element method, and so on. These methods only use a few degrees of freedom to approximate the solutions and do not allow enrichments. As a result, they typically give a limited accuracy and stability for complex media without scale separation, high contrast, and high Peclet number.
In this project, our focus is to develop accurate and stable reduced-order models for a coupled flow and transport in heterogeneous media. To achieve a desirable accuracy, we will design a systematic approach for computing multiscale basis functions for both flow and transport equations. This construction will be based on the analysis and will provide apriori error bounds. In multiscale problems, time and space adaptivity is essential as some regions may require a very few basis functions (as in numerical homogenization), while other regions may require more basis functions at certain time instants. For this, we will construct computable error indicators, to adaptively enhance the solutions in some localized regions. Due to high Peclet number, a multiscale stabilization is required. We will achieve it with a judicious construction of multiscale test functions.
The proposed research provides a novel model reduction method for coupled flow and transport problems in "real-world" porous media with non-separable scales and high contrast. Our approaches can be used as a modeling tool to identify important parameters (in terms of basis functions) in a continuum coarse-scale modeling. Our novel techniques avoid idealized scale concepts, such as Darcy scale, and help us seamlessly without postulating any assumptions to transition from pore-scale to the continuum scales. We expect that our methodology will provide an accurate and efficient tool for many real applications involving flow and transport in porous media.
在多孔介質運輸的過程中流是不能分離的。輸運方程往往是對流為主，對流通過多尺度速度場驅動。由於尺度，在速度場高變化，和高Peclet數的差距，解決這些多尺度輸運方程是非常具有挑戰性的計算。此外，人們還需要解析速度場，其中包括多尺度和高對比度的精細尺度特徵。因此，顯影降階模型，是穩定的和精確的，但在許多應用中，包括材料科學，過濾，膜應用，地下水水文，石油工程，等一個具有挑戰性的任務。有許多的傳統方法，其中包括的數值均化，數值的升頻，多尺度有限元法，等等。這些方法只用幾個自由度來近似的解決方案和不允許富集。其結果是，它們通常給一個有限的精度和穩定性為複雜的媒體沒有標分離，高對比度和高Peclet數。
在這個項目中，我們的重點是制定對非均勻介質耦合流動和運輸的準確和穩定的降階模型。為了達到理想的準確性，我們將設計計算多尺度的基礎功能都流和輸運方程系統的方法。這種結構將被分析的基礎上，將提供先驗誤差界限。在多尺度的問題，時間和空間的適應性是必要的，因為一些地區可能需要很少的基本函數（如數值同質化） ，而其他地區可能需要在某一時刻的更多的基礎功能。為此，我們將建立可計算的誤差指標，自適應地增強一些局部區域的解決方案。由於高Peclet數，需要一個多尺度穩定化。我們將與多尺度測試功能明智建設實現它。
我們提出的研究提供了與非分離尺度和高對比度的耦合流動和運輸問題，在“現實世界”多孔介質一種新的降階方法。我們的方法可以作為一個建模工具，以確定重要的參數（在基函數）在一個連續粗尺度模型。我們的新技術避免理想化規模的概念，如Darcy模型，並幫助我們實現從孔隙尺度過渡到連續尺度。我們希望我們的方法將提供涉及多孔介質流動和運移許多實際應用的準確和有效的工具。
Amount: HKD 326,800
Funding type: research
Funder scheme: General Research Fund
End date: 2019-12-31
Investigator: Eric Tsz-shun Chung
Institution: The Chinese University of Hong Kong
Funded outputs count: 7
Funder award ID: 14317516
OpenAlex ID: G1069475896