Finite Volume Element Methods for Flow Problems in Porous Media

Chou0074259研究了有限体积元方法的收敛、稳定性和超收敛问题，并用软件实现了算法。建立了不规则网格上混合控制体方法的通用框架。此外，还研究了非线性体积方法在抛物型微分方程解和积分微分方程组中的应用。地下油藏渗流中的化学或放射性污染物运移、采油过程中的驱油和含水层的生物修复等流体流动问题是复杂的，很难用计算来模拟。然而，它们对环境和能源管理都很重要。研究人员开发、分析和实现了一类名为有限体积元的计算方法，这种方法似乎比其他方法有一些优势，但还没有得到严格的分析。项目中进行的分析应该为这些方法奠定坚实的理论基础。这对于用这些方法进行的计算的可靠性和有效性是很重要的。

Chou0074259 The investigator studies the convergence, stability, and superconvergence of finite volume element type methods, and implements algorithms in software. A general framework is developed for mixed control volume methods on irregular grids. Furthermore, nonlinear covolume methods applied to parabolic differential and integro-differential equations are studied. Fluid flow problems such as chemical or radioactive contaminant transport in subsurface reservoir flow, displacement of oil in the oil recovery process, and bioremediation of aquifers, are complex and difficult to simulate computationally. Yet they are important for the environment and for managing energy resources. The investigator develops, analyzes, and implements a class of computational methods called finite volume element methods that seem to have some advantages over other methods but that have not been rigorously analyzed yet. The analysis undertaken in the project should establish a firm theoretical footing for the methods. This is important for the reliability and validity of computations performed with the methods.