王晓东副教授学术报告

报告题目：A phenomenological phase-field modeling of the crystal growth of semi-crystalline polymers

报告人:  王晓东副教授 （西北工业大学）

报告时间: 2019年12月7日（周六）下午14:30—15:30

报告地点: 数学院大会议室341

内容摘要：

Phase-field methods have been widely used to model the physical phenomena of crystal growth, phase separation, fracture, evaporation, and so on. In this talk, I will show you a phenomenological phase-field modeling of the crystal growth of semi-crystalline polymers. The model couples a nonconserved crystal order parameter with a temperature field generated by latent heat of crystallization, and obtains its model parameters from the real material parameters. Unlike the models of metals and small molecular compounds, the current model considers the partially crystallization property of semi-crystalline polymers. Moreover, due to the long-chain molecular structure, polymer crystallizations usually exhibit complex anisotropy and have polymorphous nature. To account for the various anisotropy of interfacial energy in 3D, three anisotropic functions describing the anisotropic interfacial growth patterns are deduced phenomenologically based on a number of existing experimental facts. Simulation results have preliminary demonstrated the good performance of our phase-field model in reproducing the complex and diverse morphology of semi-crystalline polymer.

报告人简介:

王晓东，西北工业大学数学与统计学院副教授，主要从事复杂流体相关的建模与计算、偏微分方程的数值求解方法、计算流体力学、计算流变学等研究。2003~2007年在西北工业大学信息与计算科学专业读本科，2006年与学校签订留校协议，2007~2014年在职攻读硕士和博士学位，期间于2010年4月正式留校任教，2016~2018年在北京大学从事博士后研究。作为项目负责人主持省部级以上科研项目7项，其中包含2项“国家自然科学基金面上项目”和1项“国家自然科学基金青年基金项目”。参与“国家重点基础研究发展计划(973计划)”、“国家自然科学基金重大项目”和“国家自然科学基金重大研究计划重点项目”各1项。在Journal of Chemical Physics，International Journal of Heat and Mass Transfer，Polymers，Physical Review E，Journal of Non-Newtonian Fluid Mechanics等重要国际期刊上发表学术论文30余篇。获陕西省高等学校科学技术奖一等奖1项、中国人民解放军科学技术进步奖三等奖1项，先后被评为2010年度理学院优秀青年教师，2013年度理学院先进工作者。博士期间，获得“教育部博士研究生学术新人奖”、“陕西省计算数学研究生学术论坛优秀论文一等奖”、“西北工业大学顶尖博士研究生奖励”等荣誉，博士论文被评为“陕西省优秀博士学位论文”。博士后期间，获得中国博士后科学基金第十批特别资助和中国博士后科学基金第60批面上资助(1等)。入选陕西省高校科协青年人才托举计划。

李晓丽博士后学术报告

报告题目：Error Analysis and Numerical Simulations of High-Precision Finite Difference Algorithms for Complex Dissipative Systems

报告人:  李晓丽博士后 （厦门大学）

报告时间: 2019年12月7日（周六）下午15:30—16:10

报告地点: 数学院大会议室341

内容摘要：

In this talk, we shall first present construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously that scheme is second-order in both time and space in various discrete norms. When equipped with an adaptive time strategy, the SAV/CN-BCFD scheme is accurate and extremely efficient. Then we will discuss how to construct a numerical scheme based on the SAV approach in time and the MAC discretization in space for the Cahn-Hilliard-Navier-Stokes phase field model, and carry out stability and error analysis. We also present the recent work on the SAV approach for the Navier-Stokes equations. Finally the numerical simulations are demonstrated the robustness and accuracy of our scheme.报告人简介:

李晓丽， 厦门大学博士后，合作导师沈捷教授。2018年12月山东大学博士毕业，主要研究领域为偏微分方程数值解与计算流体力学，已在SIAM J. Numer. Anal., Math. Comput., Comput. Methods Appl. Mech. Engrg.等计算数学高水平期刊上发表学术论文30余篇，其中以第一作者或通讯作者发表25篇。获得中国工业与应用数学学会第16届年会优秀学生论文奖，山东省研究生优秀科技成果二等奖。2019年入选“博士后创新人才支持计划”，获国家自然科学青年基金以及第65批中国博士后科学基金一等资助。

李宏伟 副教授学术报告

报告题目：An efficient second-order linear scheme for the phase field model of corrosive dissolution

报告人:  李宏伟 副教授（山东师范大学）

报告时间: 2019年12月7日（周六）下午16:10—16:50

报告地点: 数学院大会议室341

内容摘要：

内容摘要：（可附页）

We propose an efficient numerical scheme for solving the phase field model (PFM) of corrosive dissolution that is linear and second-order accurate in both time and space. The PFM of corrosion is based on the gradient flow of a free energy functional depending on a phase field variable and a single concentration variable. While classic backward differentiation formula (BDF) schemes have been used for time discretization in the literature, they require very small time step sizes owing to the strong numerical stiffness and nonlinearity of the parabolic partial differential equation (PDE) system defining the PFM. Based on the observation that the governing equation corresponding to the phase field variable is very stiff due to the reaction term, the key idea of this paper is to employ an exponential time integrator that is more effective for stiff dynamic PDEs. By combining the exponential integrator based Rosenbrock--Euler scheme with the classic Crank--Nicolson scheme for temporal integration of the spatially semi-discretized system, we develop a decoupled linear numerical scheme that alleviates the time step size restriction due to high stiffness. Several numerical examples are presented to demonstrate accuracy, efficiency and robustness of the proposed scheme in two-dimensions, and we find that a time step size of $10^{-3}$ second for meshes with the typical spatial resolution $1~\mu$m is stable. Additionally, the proposed scheme is robust and does not suffer from any convergence issues often encountered by nonlinear Newton methods.

报告人简介:

山东师范大学数学与统计学院副教授，硕士生导师。2012年获香港浸会大学博士学位，2016-2017年获国家留学基金委资助赴美国南卡罗来纳大学进行学术交流。目前主要从事相场模型和无界区域上偏微分方程数值解法的研究工作。近年来先后主持国家自然科学基金、山东省自然科学基金3项，在J. Sci. Comput., Phys. Review E等杂志上发表论文多篇。

刘争光 副教授学术报告

报告题目：Two modified SAV schemes with unconditional energy stability for phase field models

报告人:  刘争光 副教授（山东师范大学）

报告时间: 2019年12月7日（周六）下午16:50—17:30

报告地点: 数学院大会议室341

内容摘要：

we consider two novel auxiliary variable methods to obtain energy stable schemes for phase field models. The auxiliary variable based on energy bounded above does not limited to the hypothetical conditions adopted in previous approaches. We proved the unconditional energy stability for all the semi-discrete schemes carefully and rigorously. The novelty of the proposed schemes is that the computed values for the functional in square root are guaranteed to be positive. This method, termed novel auxiliary energy variable (NAEV) method does not consider any bounded below restrictions any longer. However, these restrictions are necessary in invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches which are very popular methods recently. This property of guaranteed positivity is not available in previous approaches. A comparative study of classical SAV and NAEV approaches is considered to show the accuracy and efficiency. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.报告人简介:

刘争光，山东师范大学副教授，2018年12月山东大学博士毕业，主要研究领域为非局部模型快速计算及相场模型的能量稳定算法研究，已在Comput. Methods Appl. Mech. Engrg., Appl. Math. Lett., J Sci Comput. 等计算数学知名期刊发表学术论文17篇。博士期间，参与国家科技重大专项两项，2019年以博士第一层次引进山东师范大学。