The arbitrary Lagrangian–Eulerian (ALE) method has a wide range of applications in numerical simulation of multi-material fluid flow. The indirect ALE method consists of three steps: Lagrangian step, rezone step and remapping step. In this talk, we propose two classes of high order positivity-preserving conservative remapping methods on 2D and 3D meshes in the finite volume and discontinuous Galerkin (DG) frameworks respectively. Combined with the finite volume and DG Lagrangian schemes and the rezoning strategies, we present two types of high order positivity-preserving conservative ALE methods individually. For the finite volume framework, we adopt the multi-resolution WENO reconstruction which can achieve optimal accuracy in the smooth regions and keep non-oscillatory near discontinuities. Also we incorporate an efficient local limiting to preserve positivity for the positive physical variables involved in the ALE framework without sacrificing the original high-order accuracy and conservation. For the DG framework, we develop a high-order positivity-preserving polynomial projection remapping method based on the L2 projection for the DG scheme. A series of numerical tests are provided to verify properties of our remapping algorithms, such as high-order accuracy, conservation, essential non-oscillation, positivity-preserving and efficiency. The performance of the ALE methods using the above discussed remapping algorithms is also tested for the Euler system.
成娟，北京应用物理与计算数学研究所研究员，博士生导师，北京大学应用物理与技术研究中心兼职教授。主要从事可压缩流体力学、辐射输运、多物理耦合模型高精度健壮高效数值方法研究。现为 “Journal of Computational Physics”、“Communications on Applied Mathematics and Computation”、“计算数学”、“计算物理”期刊编委、北京计算数学学会副理事长、CSIAM竞赛工作委员会副主任。主持国家自然科学基金重点项目。曾获航空航天工业部科技进步奖二等奖与中国工程物理院科技创新奖二等奖。应邀在“第十七届CSIAM年会”等国内外学术会议上作大会报告。