Highly efficient and energy stable Multi-step SAV approaches for phase field models
報告人簡介
陳艷萍，南京郵電大學博士生導師、國務院政府特殊津貼專家、教育部新世紀人才。中國工業與應用數學學會油水資源數值方法專業委員會副主任、國際數學建模挑戰賽專家委員會和學術及顧問委員、 國際 SCI 學術期刊《AAMM》編委。主持獲得教育部自然科學二等獎和廣東省科學技術二等獎、參與獲得國家教學成果二等獎和教育部自然科學一等獎等等。2014-2023 年連續 10 年入選 Elsevier 中國高被引學者榜單，入選 2023 全球頂尖前 10 萬科學家排名和數學類全球前 2%頂尖科學家榜單。主持國家自然科學基金重點項目 1 項和面上項目 8 項。
內容簡介
Recently, the scalar auxiliary variable (SAV) approach and its extended SAV-based approaches have been widely used to simulate a series of phase field models. However, many SAV-based schemes are known for the stability of a ‘modified’ energy. In this paper, we construct a series of modified SAV approaches with unconditional energy dissipation law based on several improvements to the traditional SAV approach. Firstly, by introducing the three-step technique, we can reduce the number of constant coefficient linear equations that need to be solved at each time step, while retaining all of its other advantages. Secondly, the addition of energy-optimized technique and SAV/Lagrange multiplier technique can make the numerical schemes have the advantage of preserving the original energy dissipation. Thirdly, we use the first-order approximation of the energy balance equation in the GSAV approach, instead of discretizing the dynamic equation of the auxiliary variable, so that we can construct the high-order unconditional original energy stable numerical schemes. Finally, representative numerical examples show that the efficiency and accuracy of the proposed schemes are improved.
