講座主題：Efficient and high-order algorithms with new relaxation for two-phase incompressible flows
專家姓名：李曉麗
工作單位：山東大學(xué)
講座時間：2024年04月20日 15:00-15:30
講座地點：數(shù)學(xué)與信息科學(xué)學(xué)院341
主辦單位：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
In this talk we present a class of fully decoupled and high-order implicit-explicit (IMEX) schemes for the two-phase incompressible flows based on the generalized scalar auxiliary variable approach with a new relaxation for Cahn-Hilliard equation and consistent splitting method for Navier-Stokes equation. These schemes are linear, fully decoupled, unconditionally energy stable, only require solving a sequence of elliptic equations with constant coefficients at each time step, and provide a new technique to preserve the consistency between original energy and modified energy. We derive that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. Furthermore, we carry out a rigorous error analysis for the first-order scheme and establish optimal global error estimates for the phase function, velocity and pressure in two and three-dimensional cases. Numerical examples are presented to validate the proposed schemes.
主講人介紹：
李曉麗，山東大學(xué)教授，博士生導(dǎo)師，國家高層次青年人才入選者，山東大學(xué)杰出中青年學(xué)者。中國數(shù)學(xué)會計算數(shù)學(xué)分會常務(wù)理事。主要研究領(lǐng)域為相場模型高精度算法與計算流體力學(xué)。在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comp., J. Fluid Mech., Math. Mod. Meth. Appl. Sci.及J Comput. Phys.等計算數(shù)學(xué)高水平期刊上發(fā)表學(xué)術(shù)論文多篇。2019年入選“博士后創(chuàng)新人才支持計劃”，主持國家自然科學(xué)基金面上項目、青年項目等。
