应pc加拿大预测准确率邓伟华教授的邀请，浙江大学数学科学学院张庆海教授将于近期访问我校，期间将做学术报告。

报告题目：A Fourth-order Projection Method for Solving Incompressible Navier-Stokes Equations with Adaptive Mesh Refinement and Parallel Computing

时  间：2018年12月24日下午3点

地  点：齐云楼911室

报告摘要： A generic projection maps one vector to another such that their difference is a gradient field and the projected vector does not have to be solenoidal. Via a commutator of Laplacian and the generic projection, the incompressible Navier-Stokes equations (INSE) is reformulated as the sole evolution of a divergent velocity, with the incompressibility constraint enforced by a pressure Poisson equation so that the dissipation of velocity divergence is governed by a heat equation. This prominent advantage is illustrated by straightforward formations of a semi-implicit time-stepping scheme and another explicit time-stepping scheme. with fourth-order accuracy both in time and in space. This formulation leads to a fourth-order projection method of optimal complexity: the CPU time of advancing the solution within each time step is linearly proportional to the number of control volumes. As another prominent advantage of this formulation, it is trivial to adopt another time integrator for an even higher order of accuracy. This finite-volume solver is further augmented with parallel computing and adaptive mesh refinement.

报告题目：MARS: An Analytic and Computational Framework of Interface

Tracking and Topology Computing for Multiphase Flows

时  间：2018年12月24日下午7点

地  点：齐云楼911室

报告摘要： Current Interface tracking (IT) methods avoid geometrical and topological problems by converting them into problems of numerical PDEs. In drastic comparison, our approach is to tackle geometric and topological problems with tools in geometry and topology. For this purpose, we propose MARS, a novel analytic framework based on a topological space (the Yin space) that models physically meaningful material regions. This Yin space is further strengthened by the donating region theory for analyzing current IT methods, and it is also equipped with Boolean algebra and corresponding algorithms for developing new IT methods. MARS is the first of its kind in that it relates different branches of mathematics to serve the simulation of multiphase flows. For standard benchmark problems on both IT and curvature estimation, our MARS methods are more accurate and efficient than current methods by many orders of magnitudes. We also show that, for certain water-wave problems with topological changes, our model converges to experimental results while those based on current IT methods cannot.

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报告人介绍

张庆海，1998年获清华大学学士学位，2001年获清华大学工学硕士学位，2008年获美国Cornell大学博士学位。之后在美国劳伦斯伯克利国家实验室从事计算数学方面的研究。2012年起任美国犹他大学数学系科研助理教授。2016年初开始任浙江大学数学学院教授。主要研究领域是与多相流相关的计算数学，重点是高精度自适应并行有限体积法、边界追踪问题、计算拓扑、流固耦合以及算法的数学分析。同时用数值模拟的手段研究一些具有重大意义的实际问题，如海啸模拟和甲壳类动物游泳等等。在国际高影响力期刊上发表SCI论文数十篇，包括SIAM Review, PNAS, CMAME, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing，Journal of Computational Physics等重要期刊。

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