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  報(bào)告題目：Supplementary variable method (SVM) for thermodynamically consistent partial differential equations

    主講人：龔躍政副研究員（南京航空航天大學(xué)）      

    時(shí)間：2021年5月22日（周六）9:00 a.m.

  形式：線上講座      

  講座鏈接：https://meeting.tencent.com/s/LDQPb5WRg2zD

    主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)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.

      主講人簡(jiǎn)介：    

龔躍政，博士，南京航空航天大學(xué)理學(xué)院數(shù)學(xué)系副研究員。2015年6月獲得南京師范大學(xué)計(jì)算數(shù)學(xué)博士學(xué)位。2015年7月-2017年8月在北京計(jì)算科學(xué)研究中心做博士后。2018年獲得江蘇省工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)第二屆“工業(yè)與應(yīng)用數(shù)學(xué)獎(jiǎng)青年獎(jiǎng)”，2020年入選校“長(zhǎng)空之星”計(jì)劃。目前主要從事偏微分方程的保結(jié)構(gòu)算法理論及其在計(jì)算流體相場(chǎng)模型中的應(yīng)用研究。作為項(xiàng)目負(fù)責(zé)人承擔(dān)國(guó)家自然科學(xué)基金青年項(xiàng)目、江蘇省自然科學(xué)基金青年項(xiàng)目和江蘇省“大規(guī)模復(fù)雜系統(tǒng)數(shù)值模擬”重點(diǎn)實(shí)驗(yàn)室重點(diǎn)項(xiàng)目各1項(xiàng)。參與國(guó)家自然科學(xué)基金面上項(xiàng)目1項(xiàng)。已在SIAM J. Sci. Comput.、SIAM J. Numer. Anal.、J. Comput. Phys.、Comput. Methods Appl. Mech. Eng.、中國(guó)科學(xué)等權(quán)威雜志上發(fā)表SCI學(xué)術(shù)論文40篇。