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ASecond-Order Finite-Difference Method for compressible fluids in Domains with Moving Boundaries

Communications in Computational Physics 2018年第1期23卷 230-263页

作者： Alina Chertock Armando Coco Alexander Kurganov Giovanni Russo Department of Mathematics North Carolina State UniversityRaleighNC 27695USA Department of Mechanical Engineering and Mathematical Sciences Oxford Brookes UniversityOxford OX331HXUK Department of Mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China and Mathematics DepartmentTulane UniversityNew OrleansLA 70118USA Dipartimento diMatematica ed Informatica Universit`a di Catania95125CataniaItaly.

In this paper,we describe how to construct a finite-difference shockcapturing method for the numerical solution of the Euler equation of gas dynamics on arbitrary two-dimensional domainΩ,possibly with moving *** boundaries of the domain are assumed to be changing due to the movement of solid objects/obstacles/*** the motion of the boundary could be coupled with the fluid,all of the numerical tests are performed assuming that such a motion is prescribed and independent of the fluid *** method is based on discretizing the equation on a regular Cartesian grid in a rectangular domainΩ_(R)⊃Ω.Ωe identify inner and ghost *** inner points are the grid points located insideΩ,while the ghost points are the grid points that are outsideΩbut have at least one neighbor insideΩ.The evolution equations for inner points data are obtained from the discretization of the governing equation,while the data at the ghost points are obtained by a suitable extrapolation of the primitive variables(density,velocities and pressure).Particular care is devoted to a proper description of the boundary conditions for both fixed and time dependent *** numerical experiments are conducted to illustrate the validity of themethod.Ωe demonstrate that the second order of accuracy is numerically assessed on genuinely two-dimensional problems.

关键词： compressible fluids Euler equations of gas dynamics ghost-cell extrapolation moving boundaries finite-difference shock-capturing methods

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Propagation of Density-Oscillations in Solutions to the compressible Navier-Stokes-Poisson System

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Chinese Annals of Mathematics,Series B 2008年第5期29卷 501-520页

作者： Zhong TAN Yanjin WANG Department of Mathematics Xiamen University Xiamen 361005 Fujian China Department of Mathematics Xiamen UniversityXiamen 3610051 Fujian China

Concerning a bounded sequence of finite energy weak solutions to the compressible Navier-Stokes-Poisson system (denoted by CNSP), which converges up to extraction of a subsequence, the limit system may not be the same system. By introducing Young measures as in [6, 15], the authors deduce the system (HCNSP) which the limit functions must satisfy. Then they solve this system in a subclass where Young measures are convex combinations of Dirac measures, to give the information on the propagation of density-oscillations. The results for strong solutions to (CNSP) (see Corollary 6.1) are also obtained.

关键词： compressible fluids Navier-Stokes-Poisson equations Young measures Propagation of oscillations Strong solutions

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Optimal Time Decay of Navier–Stokes Equations with Low Regularity Initial Data

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Acta Mathematica Sinica,English Series 2018年第5期34卷 855-872页

作者： Jun Xiong JIA Department of Mathematics Xi’an Jiaotong University Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS)

In this paper, we study the optimal time decay rate of isentropic Navier-Stokes equations under the low regularity assumptions about initial data. In the previous works about optimal time decay rate, the initial data need to be small in H^[N/2]＋2（R^N）. Our work combined negative Besov space estimates and the conventional energy estimates in Besov space framework which is developed by Danchim Through our methods, we can get optimal time decay rate with initial data just small in B^N/2-1,N/2＋1∩^N/2-1,N/2 and belong to some negative Besov space （need not to be small）. Finally, combining the recent results in [25] with our methods, we only need the initial data to be small in homogeneous Besov space B^N/2-2,N/2 ∩B^N/2-1 to get the optimal time decay rate in space L2.

关键词： compressible fluids besov space framework optimal time decay negative Besov space

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A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

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Science China Mathematics 2012年第2期55卷 245-275页

作者： DANCHIN Raphaeel LAMA UMR 8050 Universitg Paris-Est 61 avenue du Gdn@al de Gaulle 94010 Crdteil Cedex France

Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey paper, we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space. We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.

关键词： compressible fluids critical regularity Besov spaces Fourier analysis Mach number

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