講座主題：Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities
專(zhuān)家姓名：何曉明
工作單位：山東大學(xué)
講座時(shí)間：2024年06月05日16:30-17:30
講座地點(diǎn)：數(shù)學(xué)與信息科學(xué)學(xué)院341
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
In this presentation, we consider the numerical modeling and simulation via the phase field approach for coupled two-phase free flow and two-phase porous media flow of different densities and viscosities. The model consists of the Cahn-Hilliard-Navier-Stokes equations in the free flow region and the Cahn-Hilliard-Darcy equations in porous media that are coupled by several domain interface conditions. It is showed that the coupled model satisfies an energy law. Then we first propose a coupled unconditionally stable finite element method for solving this model and analyze the energy stability for this method. Furthermore, based on the ideas of pressure stabilization and artificial compressibility, we propose an unconditionally stable time stepping method that decouples the computation of the phase field variable, the velocity and pressure of free flow, the velocity and pressure of porous media, hence significantly reduces the computational cost. The energy stability of this decoupled scheme with the finite element spatial discretization is rigorously established. We verify numerically that our schemes are convergent and energy-law preserving. Numerical experiments are also performed to illustrate the features of two-phase flows in the coupled free flow and porous media setting.
主講人介紹：
何曉明,，美國(guó)密蘇里科技大學(xué)教授,。2002年與2005年在四川大學(xué)數(shù)學(xué)學(xué)院分別獲學(xué)士與碩士學(xué)位,， 2009年在弗吉尼亞理工大學(xué)數(shù)學(xué)系獲博士學(xué)位,，2009年至2010年在佛羅里達(dá)州立大學(xué)作博士后,。2010年至2016年在美國(guó)密蘇里科學(xué)技術(shù)大學(xué)任助理教授,，2016年晉升為副教授并獲終身教職,，2021年晉升為正教授,。2018年獲得Humboldt Research Fellowship for Experienced Researchers,。擔(dān)任計(jì)算數(shù)學(xué)領(lǐng)域國(guó)際期刊International Journal of Numerical Analysis & Modeling的Managing editor,。從2012年起主持了多項(xiàng)由美國(guó)國(guó)家科學(xué)基金會(huì)和美國(guó)能源部資助的科研項(xiàng)目。2014-2016年擔(dān)任SIAM美國(guó)中部分會(huì)的第一任主席和前兩屆年會(huì)的組織委員會(huì)主席,。2019年起擔(dān)任Midwest Numerical Analysis Day的組織委員成員,。2021年1月起擔(dān)任SIAM Committee on Programs and Conferences成員。2021年7月起擔(dān)任密蘇里科技大學(xué)Vice Chancellor of Research and Innovation辦公室的Faculty Fellow。何曉明教授主要的研究領(lǐng)域是計(jì)算科學(xué)與工程,。研究問(wèn)題主要包括界面問(wèn)題,，計(jì)算流體力學(xué)，計(jì)算電磁學(xué),，有限元方法,，各類(lèi)解耦算法，數(shù)據(jù)同化,，隨機(jī)偏微分方程,，控制問(wèn)題等。他將計(jì)算數(shù)學(xué)與實(shí)際工程應(yīng)用問(wèn)題結(jié)合起來(lái),，在科學(xué)計(jì)算和應(yīng)用領(lǐng)域做了大量的工作,，在SIAM Journal on Scientific Computing，Journal of Computational Physics,，Computer Methods in Applied Mechanics and Engineering, SIAM Journal on Numerical Analysis,， Mathematics of Computation，Numerische Mathematik,，IEEE Transactions on Plasma Science, Lab on a Chip, Langmuir, Energy & Fuels, Computational Materials Science等雜志發(fā)表論文90余篇,。
