Speaker: Prof. Qiang Zhang (张强教授)

Time: 15:00-16:00, 24 April 2025 (Thursday)  (Beijing time)

Venue: A103,  Lijiao Building

Abstract

Richtmyer-Meshkov 不稳定性是流体力学中的经典问题。它是由激波所驱动的流体界面混合。可压缩流体中的这种不稳定性是一种非常复杂的现象。它在两种不同密度流体之间的物质界面上产生不稳定的指状结构，称为尖峰和气泡。尖峰是重流体渗透到轻流体中的部分，而气泡是轻流体渗透到重流体中的部分。自 1960 年以来，研究人员一直在寻找理论来准确地预测可压缩流体间不稳定物质界面上尖峰和气泡的增长率。理论研究的困难在于流体是可压缩的，物质界面是不稳定的，物质界面的动力学是非线性的。数值模拟一直是研究可压缩流体中 Richtmyer-Meshkov 不稳定性中手指增长的主要工具。理论研究通常将流体近似为不可压缩的，将入射冲击波近似为冲击力。这种近似会导致定性的错误预测。在本次演讲中，我们将介绍可压缩流体中 Richtmyer-Meshkov 不稳定性增长率的理论。我们的理论方法包括分析不稳定材料界面的动力学行为，推导出早期和晚期的解析表达式，然后进行渐近匹配。我们的理论不包含拟合参数，适用于尖峰和气泡、适用于可压缩流体、适用于任意密度比的系统、适用于任意强度的入射冲击波以及从早期到晚期的整个演化过程。理论预测与数值模拟结果和实验数据高度一致。即使对于入射激波马赫数高达 15.3 的可压缩流体系统，我们的理论预测仍然与数值模拟数据高度一致。

About the Speaker

Professor Zhang is a professor in the BNBU Financial Mathematics Programme, and a senior member at the Research Center for Mathematics. Professor Zhang received his Bachelor from Fudan University and his Master and Ph.D. from New York University. He is among the first group of CUSPEA students admitted to American universities. After graduation he has been working at Courant Institute of Mathematics at New York University, State University of New York at Stony Brook, City University of Hong Kong where he had a joint appointment in Department of Mathematics and Department of Economics and Finance.  Professor Zhang has broad research interests that include mathematical finance, fluid dynamics, scientific computing, granular materials, and physics. For each of these fields, his research results have been published in top journals.