报告名称：Numerical solutions for a Phase Field Model with Peng-Robinson Equation of State

主办单位：数学与统计学学院

报告专家：彭秋瑾

专家所在单位：许昌学院

报告时间：2019年12月6日下午16：00—17:00

报告地点：数学与统计学学院203报告厅

专家简介：彭秋瑾，许昌学院数学与统计学院讲师，2009年本科毕业于湖北大学数学与计算机学院数学与应用数学专业（师范类），2012年硕士毕业于北京师范大学数学科学学院计算数学专业，2016年博士毕业于香港理工大学应用数学系，2016年至2018年在中国人民大学数学科学研究院从事博士后工作。先后主持人民大学新教师启动基金项目、中国博士后基金资助项目，目前主持国家自然科学基金青年科学基金项目。主要研究领域是复杂流体的建模和计算。目前涉及领域有高分子水凝胶的相变的建模和计算、基于石油流体状态方程的抛物方程高效、能量稳定的数值格式的设计和分析。目前在Journal on Scientific Computing（中科院二区）, Communications in Computational Physics（中科院大类三区，小类二区）等期刊发表SCI论文6篇。

报告摘要：This work is concerned with mathematical modeling and numerical simulations of the steady state and the movements of complex fluids involved in oil exploitation practice. Capillary pressure caused by surface tension at the interface between every two adjacent different phases of the mixture is viewed as the leading force in oil recovery from fractured oil reservoirs. Therefore, the interface between contiguous phases has become a critical mathematical modeling aspect.

The phase field model has been widely applied to model or understand the interface between different phases of oil mixture. Based on the assumption that the density of every substance is continuous over the whole fluid region, the total Helmholtz free energy often contains the homogeneous part and the gradient contribution part. Based on the original total free energy, the equilibrium state and the kinetic processes could be determined according to thermodynamic principles.

As for the fluid system related to the oil recovery process, we apply the homogeneous free energy density and the parameters of the gradient part of the free energy density provided by the widely used Peng-Robinson equation of state (EOS). The gradient flow equation based on this energy functional are presented and solved by several energy stable schemes. The theoretical analyses of these numerical schemes and numerical results demonstrate good properties of these numerical schemes.

邀请人：向妮

是否涉外：否