报告题目：Supplementary variable method (SVM) for thermodynamically consistent partial differential equations

主讲人：龚跃政副研究员（南京航空航天大学）      

时间：2021年5月22日（周六）9:00 a.m.

形式：线上讲座      

讲座链接：https://meeting.tencent.com/s/LDQPb5WRg2zD

主办单位：统计与数学学院

      摘要：In this talk, we present a new paradigm for developing structure-preserving algorithms for thermodynamically consistent partial differential equation (TCPDE) system, called the supplementary variable method (SVM). We add a proper number of supplementary variables to the TCPDE system coupled with its energy equation and other deduced equations through perturbations to arrive at a consistent, well-determined, solvable and structurally stable system. The extended system not only reduces to the TCPDE system at specific values of the supplementary variables, but also allows one to retain consistency and solvability after a consistent numerical approximation. Among virtually infinite many possibilities to add the supplementary variables, we present two that maintain thermodynamical consistency in the extended system before and after the approximation. The new schemes are compared with the energy stable SAV scheme and the fully implicit Crank-Nicolson scheme. The numerical results favor the new schemes in the overall performance.

      主讲人简介：    

龚跃政，博士，南京航空航天大学理学院数学系副研究员。2015年6月获得南京师范大学计算数学博士学位。2015年7月-2017年8月在北京计算科学研究中心做博士后。2018年获得江苏省工业与应用数学学会第二届“工业与应用数学奖青年奖”，2020年入选校“长空之星”计划。目前主要从事偏微分方程的保结构算法理论及其在计算流体相场模型中的应用研究。作为项目负责人承担国家自然科学基金青年项目、江苏省自然科学基金青年项目和江苏省“大规模复杂系统数值模拟”重点实验室重点项目各1项。参与国家自然科学基金面上项目1项。已在SIAM J. Sci. Comput.、SIAM J. Numer. Anal.、J. Comput. Phys.、Comput. Methods Appl. Mech. Eng.、中国科学等权威杂志上发表SCI学术论文40篇。