An conservative and robust finite element reconstruction method for simulating incompressible Navier-Stokes equations
报告题目：An conservative and robust finite element reconstruction method for simulating incompressible Navier-Stokes equations
报告专家：芮洪兴（山东大学）
报告时间：2023年5月22日16:50-17:50
报告地点：四川大学数学学院409报告厅
报告摘要：
Proper EMA-balance (E: kinetic energy; M: momentum; A: angular momentum), pressure-robustness and Re-semi-robustness (Re: the Reynolds number) are important properties of incompressible Navier-Stokes simulations with exactly divergence-free finite elements. However, the construction of these elements is not trivial in most cases. In this talk, based on the pressure-robust reconstruction methods in [For example, A. Linke et al, Comput. Methods Appl. Mech. Engrg. 2016], we propose a novel reconstruction method for a class of non-divergence-free simplicial elements which admits almost all the above properties. The only exception is the energy balance where kinetic energy should be replaced by a properly discrete form. Numerical comparisons with exactly divergence-free methods, pressure-robust reconstructions and the EMAC scheme are provided to confirm our theoretical results.
We also present other reconstruction method with different conservative properties.
专家简介：
芮洪兴，二级教授，博士生导师。主要从事计算数学的方法、理论及应用研究。主持国家自然科学基金重点目、面上项目、国家重点研发项目子课题、中石化勘探院委托任务等多项。在计算数学三大顶刊Numer Math、SIAM J Numer Anal、Math Comp，流体力学顶刊J Fluid Mech等发表多篇高水平论文，参编专著3部。获教育部自然科学一等奖、山东省自然科学二等奖（首位）、教育部自然科学二等奖（首位）。
曾任CSIAM常务理事、油水资源数值方法专委会主任，中国计算数学学会常务理事。现任中国计算物理学会常务理事、山东省工业与应用数学会副理事长、山东数学会计算数学专委会主任。
邀请人：陈刚