青年学术论坛邀请报告

摘要:
流体中的最优形状设计问题是微分几何、形状优化理论和计算流体力学有机结合的产物. 随着计算流体动力学的飞速发展以及计算机性能的不断提高，基于计算流体动力学的最优形状设计已成为当前计算流体力学研究的一个重要领域. 本报告主要以Navier-Stokes 方程作为流体优化问题的控制方程，利用连续共轭法和离散共轭法对耗散能极小化形状优化问题进行系统深入的研究，借助于速度法描述区域扰动，从而建立优化问题的一阶最优性条件并给出数值求解算法及其在翼型设计、血流插管设计以及一般绕流物体设计中的应用.


Abstract: Optimal shape design for fluids is a combination of differential geometry, shape optimization and computational fluid dynamics (CFD). With the rapid development of CFD and enhanced performance of the computers, these problems are of great importance in CFD. The adjoint methods for two kinds of shape optimization problems controlled by the Navier-Stokes equations have been systematically studied in this talk. The first order optimality conditions of the shape optimization problems are established in virtue of the velocity method. The numerical algorithms and the corresponding simulations are given with applications in wing design, cannula optimization and optimization of a body located in fluid flow.