Qinghai Zhang, Professor, Zhejiang University.

Shipeng Mao, Professor

A fourth-order energy-stable projection method for numerically solving the incompressible Navier-Stokes equations with prescribed moving boundaries

8:30-9:30 April 22(Monday), S723

We first propose a reformulation of the incompressible Navier-Stokes equations (INSE) with no-slip conditions so that the main evolutionary variable is a divergent velocity with its divergence decaying exponentially. Then we couple this GePUP (generalized projection method with unconstrained PPE) formulation with SAV (Scalar Auxiliary Variable) and SDIRK to obtain energy stability and fourth-order accuracy in velocity. For irregular domains, we develop an AI-aided algorithm to generate a poised lattice on Cartesian grids so that the least-square discretization of spatial operators strikes a balance between efficiency and good-conditioning. We further augment the solver for INSE on moving domains and show fourth-order convergence in velocity. Applications to interval wave propagation in South China Sea will be discussed.

报告人介绍：张庆海，浙江大学数学学院教授。 清华大学学士及硕士，美国康奈尔大学（Cornell University）博士，美国劳伦斯伯克利国家实验室博士后。国家级青年人才，国家级科技创新领军人才。主要研究方向为动边界不可压流体的理论建模和数值计算，工作聚焦点为应用拓扑、界面追踪和高阶有限体积方法。代表作发表在《SIAM Review》《Mathematics of Computation》《SIAM Journal on Numerical Analysis》《SIAM Journal on Scientific Computing》《PNAS》等学术刊物上。