Fully Locally Conservative Characteristic Methods for Transport Problems

化学示踪剂在环境流体（例如地下水中的污染物）中的传输可以通过欧拉-拉格朗日数值方法来近似。 这些方法局部保存示踪剂质量，但不保存周围流体的质量。 因此，他们计算不准确的密度，这可能会随着时间的推移严重降低解决方案的质量。 PI和同事最近定义了体积校正特征混合方法（VCCMM）的最简单的运输问题，考虑运输问题不是一个单一的双曲线方程的示踪剂，而是作为一个系统的两个方程描述运动的示踪剂和周围的流体，其中每一个都必须保存本地。 这个项目将：（1）完成VCCMM的开发，使之建立在一个良好的理论基础上，并开发一个软件的并行版本;（2）改进VCCMM并将其扩展到更复杂的流动;（3）开发一个网格适应版本;（4）开发非线性输运问题的方法，包括可混溶、可压缩流动和两相、不混溶流动，这些问题的解可能包含激波和稀薄。 该项目预计将导致显着改善的近似传输问题的长时间模拟，因为离散近似将有较少的数值扩散和保存重要的物理原理。该项目预计将产生更广泛的影响，包括：（1）开发一个科学软件工具，可应用于广泛的实际问题;（2）培养一名博士。学生在多学科的环境;和（3）社会效益，允许更好的建模，例如，地质盆地形成、长寿命放射性同位素衰变、可混溶指状和两相流。在许多应用中，预测被称为示踪剂的化学物质在另一种环境流体中的运动的能力是重要的。 例如，在地下水污染物迁移研究中出现了这种需要。 本项目研究通过计算机模拟改进示踪剂输运预测的方法。拉格朗日类型的最先进的数值算法通过明确计算空间小区域内单个粒子的运动来模拟示踪剂传输。 示踪剂质量是守恒的，这意味着没有质量是人为创建或破坏的数值计算。 这是研究的关键属性，例如，由于即使是很小的浓度也可能对人类有毒，因此示踪剂的任何产生或降解都必须是由于物理和化学过程而不是数字伪影。然而，拉格朗日方法不保存周围流体的质量。 这导致不准确的示踪剂密度。 也就是说，尽管示踪剂质量是守恒的，但其浓度被错误地计算，这可能导致反应动力学的严重不准确和预测运动随时间的退化。 PI为解决这些困难而采取的方法是考虑示踪剂和环境流体的运输，其中每一种都必须保存。 该研究预计将导致显着改善的近似运输问题的长时间模拟，并培训至少一个博士学位。学生在多学科环境中。 这项工作具有潜在的社会效益，适用于地下水污染，石油和天然气生产，二氧化碳封存的问题。

The transport of a chemical tracer within an ambient fluid (such as a contaminant in groundwater), can be approximated by Eulerian-Lagrangian numerical methods. These methods conserve tracer mass locally, but not the mass of the ambient fluid. They therefore compute inaccurate densities, which can seriously degrade the quality of the solution over time. The PI and coworker recently defined the Volume Corrected Characteristics-Mixed Method (VCCMM) for the simplest transport problem, by considering the transport problem not as a single hyperbolic equation for the tracer, but rather as a system of two equations describing the motion of both the tracer and ambient fluids, each of which must be conserved locally. This project will:(1) Complete the development of VCCMM, by placing it on a sound theoretical footing and developing a parallel version of the software; (2) Improve and extend VCCMM to more complex flows; (3) Develop a grid adapted version; and (4) Develop methods for nonlinear transport problems, including miscible, compressible flows, and two-phase, immiscible flows, for which the solution may contain shocks and rarefactions. The project is expected to result in significant improvement in the approximation of transport problems for long time simulation, because the discrete approximation will have less numerical diffusion and preserve important physical principles. The project is expected to have broader impacts, including: (1) Developing a scientific software tool that can be applied to a wide range of practical problems; (2) The training of one Ph.D. student in a multidisciplinary environment; and (3) Societal benefits by allowing better modeling of, e.g., geologic basin formation, long-lived radio-isotope decay, miscible fingering, and two-phase flows.The ability to predict the movement of a chemical specie, called a tracer, within another, ambient fluid is important in many applications. For example, the need arises in ground-water contaminant migration studies. This project investigates ways to improve the prediction of tracer transport through computer simulation. State-of-the-art numerical algorithms of Lagrangian type simulate tracer transport by explicitly calculating the movement of individual particles within small regions of space. Tracer mass is conserved, meaning that no mass is artificially created or destroyed by the numerical calculations. This is a critical property for studies involving, e.g., contaminants, since even small concentrations can be toxic to humans, and any creation or degradation of the tracer must be due to physical and chemical processes and not to numerical artifacts. However, Lagrangian methods do not conserve the mass of the ambient fluid. This results in inaccurate tracer densities. That is, although tracer mass is conserved, its concentration is incorrectly computed, which can lead to serious inaccuracies in reaction dynamics and degradation in the predicted movement over time. The approach taken by the PI to resolve these difficulties is to consider the transport of both the tracer and ambient fluids, each of which must be conserved. The research is expected to result in significant improvement in the approximation of transport problems for long time simulation, and the training of at least one Ph.D. student in a multidisciplinary environment. This work has potential societal benefits as applied to problems in the contamination of ground-water, petroleum and natural gas production, and CO2 sequestration.