講座主題：Supplementary variable method (SVM) for thermodynamically consistent partial differential equations
專家姓名：龔躍政
工作單位：南京航空航天大學
講座時間：2021年12月23日 9:00-11:00
講座地點：騰訊會議，會議ID：367 650 298
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
龔躍政，南京航空航天大學理學院數學系副研究員。2015年6月獲得南京師范大學計算數學博士學位。2015年7月-2017年8月在北京計算科學研究中心做博士后。2018年獲得江蘇省工業與應用數學學會第二屆“工業與應用數學獎青年獎”，2020年入選校“長空之星”計劃。目前主要從事偏微分方程的保結構算法理論及其在計算流體相場模型中的應用研究。作為項目負責人承擔國家自然科學基金青年項目、江蘇省自然科學基金青年項目和江蘇省“大規模復雜系統數值模擬”重點實驗室重點項目各1項。參與國家自然科學基金面上項目1項。已在SIAM J. Sci. Comput.、SIAM J. Numer. Anal.、J. Comput. Phys.、Comput. Methods Appl. Mech. Eng.、中國科學等權威雜志上發表SCI學術論文40余篇。
