Seminars on Numerical Algorithms, Analyses, and Applications: An energy-stable and conservative numerical method for multicomponent Maxwell-Stefan model

：寇继生（绍兴文理学院）
：2024-12-11 09:00
：海韵园行政楼C503

报告人：寇继生（绍兴文理学院）

时  间：2024年12月11日9:00

地  点：海韵园行政楼C503

内容摘要:

Numerical simulation of gas flow in porous media is becoming increasingly attractive due to its importance in shale and natural gas production and carbon dioxide  sequestration. Taking molar densities as the primary unknowns rather than the pressure and molar fractions, we propose an alternative formulation of multicomponent Maxwell-Stefan (MS) model with rock compressibility. Benefiting from the definitions of gas and solid free energies, this MS formulation has a distinct feature that it follows an energy dissipation law, and namely, it is consistent to the second law of thermodynamics. Additionally, the formulation obeys the famous Onsager’s reciprocal principle. An efficient energy stable numerical scheme is constructed using the stabilized energy factorization approach for the Helmholtz free energy density and certain carefully-designed formulations involving explicit and implicit mixed treatments for the coupling between molar densities, pressure and porosity. We rigorously prove that the scheme inherits the energy dissipation law at the discrete level. The fully discrete scheme has the ability to ensure the mass conservation law for each component as well as preserve the Onsager’s reciprocal principle. Numerical tests are conducted to verify our theories, and in particular, to demonstrate the good performance of the proposed scheme in energy stability and mass conservation as expected from our theories.

个人简介：

寇继生，绍兴文理学院教授，浙江省钱江学者特聘教授。主要研究方向为多孔介质中多相流和多组分流的数值模拟，油藏数值模拟相关的两相流模型及其数值计算方法,部分论文发表在Journal of Computational Physics、Computer Methods in Applied Mechanics and Engineering、SIAM Journal on Numerical Analysis、SIAM Journal on Scientific Computing等国际重要期刊上。

 

联系人：陈黄鑫