报告题目：A semi-Lagrangian meshfree method for flow problems with strong convection

报告人：王晓东 副教授

报告时间：2019年12月23日（周一）15:00—17:00    

报告地点：数学与统计学院学术报告厅

报告摘要：The flow of viscous fluids is often governed by the Navier-Stokes equation. In the Eulerian framework, both convection and diffusion terms exist in the equations. Numerical difficulties often arise when the diffusion term is dominated by the convection term. In order to obtain stable results, numerical methods with up-wind property must be used. However, for the methods derived from Galerkin projection, such as finite element method and element free Galerkin method, designing a numerical scheme with up-wind property is rather difficult. On the other hand, in the Lagrangian framework, convection term no longer presents in the equations. What we confront is pure diffusion equations, and standard Galerkin methods can be directly used in solving these equations. Although there is no difficult in solving the equations, new difficulties arise from grid deformation. A smart idea is to combine the advantages from both Eulerian and Lagrangian frameworks while eliminating the disadvantages of each. That is to solve the pure diffusion equations from Lagrangian framework on a fixed grid from Eulerian framework. Such a method is named as Eulerian–Lagrangian method or semi-Lagrangian method. In this talk, I will present a semi-Lagrangian meshfree method. Because interpolations of the meshfree method use no grid, searching algorithms will not need in interpolating the values at the departure points. In addition, constructing high order interpolation functions is trivial for the meshfree method. Therefore, the proposed method is expected having better accuracy and higher efficiency. Several numerical examples in 1D and 2D are used to verify the good performance of the new method for flow problems with strong convection.

个人简介：王晓东，西北工业大学数学与统计学院副教授，主要从事复杂流体相关的建模与计算、偏微分方程的数值求解方法、计算流体力学、计算流变学等研究。2003~2007年在西北工业大学信息与计算科学专业读本科，2007~2014年在欧阳洁教授指导下在职攻读硕士和博士学位，期间于2010年4月留校任教，2016~2018年在北京大学在张平文院士指导下从事博士后研究。作为项目负责人主持省部级以上科研项目7项，其中包含2项“国家自然科学基金面上项目”和1项“国家自然科学基金青年基金项目”。参与“国家重点基础研究发展计划(973计划)”、“国家自然科学基金重大项目”和“国家自然科学基金重大研究计划重点项目”各1项。在Journal of Chemical Physics，International Journal of Heat and Mass Transfer，Polymers，Physical Review E，Journal of Non-Newtonian Fluid Mechanics等重要国际期刊上发表学术论文30余篇。获陕西省高等学校科学技术奖一等奖1项、中国人民解放军科学技术进步奖三等奖1项，先后被评为2010年度理学院优秀青年教师，2013年度理学院先进工作者。博士期间，获得“教育部博士研究生学术新人奖”、“陕西省计算数学研究生学术论坛优秀论文一等奖”、“西北工业大学顶尖博士研究生奖励”等荣誉，博士论文被评为“陕西省优秀博士学位论文”。博士后期间，获得中国博士后科学基金第十批特别资助和中国博士后科学基金第60批面上资助(1等)。入选陕西省高校科协青年人才托举计划。

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