"九章講壇"第839講—徐巖教授

應(yīng)yl7703永利官網(wǎng)邀請，中國科學(xué)技術(shù)大學(xué)數(shù)學(xué)科學(xué)學(xué)院徐巖教授將于2024年7月8日舉辦線上學(xué)術(shù)報告。歡迎廣大師生參加。

題目：Equilliburm preserving space in discontinuous Galerkin methods for hyperbolic balance laws

時間：2024年7月8日9:00

騰訊會議ID：666815509 密碼：2407

摘要：In this paper, we develop a general framework for the design of the arbitrary high-order well-balanced discontinuous Galerkin (DG) method for hyperbolic balance laws, including the compressible Euler equations with gravitation and the shallow water equations with horizontal temperature gradients (referred to as the Ripa model). Not only the hydrostatic equilibrium, but our scheme is also well-balanced for the exact preservation of the moving equilibrium state. The strategy adopted is to approximate the equilibrium variables in the DG piecewise polynomial space, rather than the conservative variables, which is pivotal in the well-balanced property. Our approach provides flexibility in combination with any consistent numerical flux, and it is free of the reference equilibrium state recovery and the special source term treatment. Extensive numerical examples are used to validate the high order accuracy and exact equilibrium preservation for various flows given by hyperbolic balance laws. With a relatively coarse mesh, it is also possible to capture small perturbations at or close to steady flow without numerical oscillations.

報告人簡介

徐巖，中國科學(xué)技術(shù)大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授。2005年于中國科學(xué)技術(shù)大學(xué)數(shù)學(xué)系獲計算數(shù)學(xué)博士學(xué)位。2005-2007年在荷蘭Twente大學(xué)從事博士后研究工作。2009年獲得德國洪堡基金會的支持在德國Freiburg大學(xué)訪問工作一年。主要研究領(lǐng)域為高精度數(shù)值計算方法。2008年度獲全國優(yōu)秀博士學(xué)位論文獎，2017年獲國家自然科學(xué)基金委“優(yōu)秀青年基金”, 2017年獲中國數(shù)學(xué)會計算數(shù)學(xué)分會第二屆“青年創(chuàng)新獎”。徐巖教授入選了教育部新世紀(jì)優(yōu)秀人才計劃，主持國家自然科學(xué)基金面上項目、德國洪堡基金會研究組合作計劃、霍英東青年教師基礎(chǔ)研究課題等科研項目。徐巖教授擔(dān)任中國數(shù)學(xué)會計算數(shù)學(xué)分會理事，擔(dān)任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、計算物理等雜志的編委。

甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)省級重點實驗室

甘肅應(yīng)用數(shù)學(xué)中心

yl7703永利官網(wǎng)

萃英學(xué)院

2024年7月6日