數(shù)學(xué)與統(tǒng)計(jì)學(xué)院學(xué)術(shù)報(bào)告預(yù)告：Bound- and Positivity-Preserving Path-Conservative Central-Upwind AWENO Scheme for the Five-Equation Model of Compressible Two-Component Flows

報(bào)告題目：Bound- and Positivity-Preserving Path-Conservative Central-Upwind AWENO Scheme for the Five-Equation Model of Compressible Two-Component Flows

報(bào) 告 人：王保山

報(bào)告時(shí)間：12月31日10:20

報(bào)告地點(diǎn)：蓮花街校區(qū)惟德樓315會(huì)議室

報(bào)告人照片：

報(bào)告人簡(jiǎn)介：王保山，中國(guó)海洋大學(xué)數(shù)學(xué)科學(xué)學(xué)院副教授，2022年博士畢業(yè)于中國(guó)海洋大學(xué)，師從Wai Sun Don教授，主要從事雙曲守恒律方程的高精度數(shù)值方法研究，在SIAM Journal on Scientific Computing、Journal of Computational Physics等期刊上發(fā)表30余篇學(xué)術(shù)論文，博士學(xué)位論文《保物理約束的高精度WENO格式》獲評(píng)2023年度山東省優(yōu)秀博士學(xué)位論文，主持兩項(xiàng)國(guó)家級(jí)科研項(xiàng)目，參與兩項(xiàng)國(guó)家重大科技專項(xiàng)項(xiàng)目，參與Journal of Computational Physics等期刊審稿40余次。

報(bào)告內(nèi)容簡(jiǎn)介：In this talk, we propose a fifth-order finite-difference bound- and positivity-preserving (BP) path-conservative central-upwind alternative weighted essentially non-oscillatory (PCCU-AWENO) scheme for the five-equation model of compressible two-component flows. The proposed scheme is capable of maintaining the equilibrium near moving material interfaces, ensuring that velocity and pressure remain continuous at these interfaces. In addition, the scheme is designed to preserve the bound of volume fraction and positivity of density and internal energy: these three properties are absolutely essential for robustness of the proposed scheme. We first prove the BP property of the first-order PCCU scheme under a sufficient CFL condition and then introduce high-order BP limiters. The performance of the introduced PCCU-AWENO scheme is demonstrated on several one- and two-dimensional challenging numerical examples.

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數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
2024年12月27日