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SIMPLE WAVES OF THE TWO DIMENSIONAL COMPRESSIBLE FULL EULER EQUATIONS

Acta Mathematica Scientia 2015年第4期35卷 855-875页

作者：陈宇周忆 School of Mathematical Sciences Fudan University

In this paper, we establish the existence of four families of simple wave solu- tion for two dimensional compressible full Euler system in the self-similar plane. For the 2 × 2 quasilinear non-reducible hyperbolic system, there not necessarily exists any simple wave solution. We prove the result that there are simple wave solutions for this 4× 4 non- reducible hyperbolic system, its simple wave flow is covered by four straight characteristics λ0 =λ1,λA2, λ3 and the solutions keep constants along these lines. We also investigate the existence of simple wave solution for the isentropic relativistic hydrodynamic system in the self-similar plane.

关键词： simple waves Euler equations characteristic decomposition

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Two-Dimensional Riemann Problems for the Compressible Euler System

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Chinese Annals of Mathematics,Series B 2009年第6期30卷 845-858页

作者： Yuxi ZHENG Dedicated to Professor Andrew Majda for his 60th Birthday

Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult,but a viable alternative remains *** author lists merits of one-dimensional Riemann problems and compares them with those for the current two-dimensional Riemann problems,to illustrate their ***-dimensional Riemann problems are approached via the methodology promoted by Andy Majda in the spirits of modern applied mathematics;that is,simplified model is built via asymptotic analysis,numerical simulation and theoretical analysis.A simplified model called the pressure gradient system is derived from the full Euler system via an asymptotic ***-of-the-art numerical methods in numerical simulations are used to discern small-scale structures of the solutions,e.g.,semi-hyperbolic *** methods are used to establish the validity of the structure revealed in the numerical *** entire process,used in many of Majda's programs,is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws.

关键词： characteristic decomposition Guderley reflection Hodograph transform Pressure gradient system Self-similar Semi-hyperbolic wave Triple point paradox Riemann problem Riemann variable

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Rarefaction Wave Interaction and Shock-Rarefaction Composite Wave Interaction for a Two-Dimensional Nonlinear Wave System

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Chinese Annals of Mathematics,Series B 2021年第1期42卷 135-150页

作者： Geng LAI Sisi XIE Department of Mathematics Shanghai UniversityShanghai 200444China

In order to construct global solutions to two-dimensional(2 D for short)Riemann problems for nonlinear hyperbolic systems of conservation laws,it is important to study various types of wave *** paper deals with two types of wave interactions for a 2 D nonlinear wave system with a nonconvex equation of state:Rarefaction wave interaction and shock-rarefaction composite wave *** order to construct solutions to these wave interactions,the authors consider two types of Goursat problems,including standard Goursat problem and discontinuous Goursat problem,for a 2 D selfsimilar nonlinear wave *** classical solutions to these Goursat problems are obtained by the method of *** solutions constructed in the paper may be used as building blocks of solutions of 2 D Riemann problems.

关键词： Nonlinear wave system Rarefaction wave Shock-rarefaction composite wave Wave interaction characteristic decomposition

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Conical Sonic-Supersonic Solutions for the 3-D Steady Full Euler Equations

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Communications on Applied Mathematics and Computation 2023年第3期5卷 1053-1096页

作者： Yanbo Hu Xingxing Li School of Mathematics Hangzhou Normal UniversityHangzhou 311121ZhejiangChina

This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross *** the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal *** a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable *** overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph *** singular terms are isolated from the highly nonlinear complicated system and then can be handled *** establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.

关键词： Three-dimensional(3-D)full Euler equations Conical flow Conical-sonic characteristic decomposition Classical solution

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A Hybrid Compact-WENO Scheme for Solving Hyperbolic Conservation Laws

A Hybrid Compact-WENO Scheme for Solving Hyperbolic Conserva...

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第四届海峡两岸计算流体力学学术研讨会

作者： Yu-Xin Ren. Miao''er Liu and Hanxin Zhang Department of Engineering Mechanics, Tsinghua University, Beijing 100084, National Key Laboratory for CFD, Beijing 100083,

＜正＞ This paper presents a fifth order conservative hybrid compact-WENO scheme for shock capturing calculation. The hybrid scheme is considered as the weighted average of two sub-scheme: the conservative compact scheme proposed by Pirozzoli and the WENO scheme. The weight function is designed so that the abrupt transition from one sub-scheme to another is avoided and the resulting hybrid scheme is oscillation free near the flow discontinuities. A Roe type, characteristic-wise finite difference scheme is proposed which generalizes the hybrid scheme for the scalar equation to system of conservation laws. Several test cases are presented to validate the proposed scheme.

关键词： Hybrid compact-WENO scheme characteristic decomposition Euler equations.

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