A Numerical Glimpse at Some Non-standard Solutions to Compressible Euler Equations

被引：2

作者：

Chiodaroli, Elisabetta ^{[1
]}

Gosse, Laurent ^{[2
]}

机构：

[1] EPFL Lausanne, Stn 8, CH-1015 Lausanne, Switzerland

[2] CNR, IAC, Via Taurini 19, I-00185 Rome, Italy

来源：

INNOVATIVE ALGORITHMS AND ANALYSIS | 2017年 / 16卷

关键词：

NONLINEAR HYPERBOLIC SYSTEMS; SHALLOW-WATER EQUATIONS; ENTROPY SOLUTIONS; CONSERVATION-LAWS; WELL-POSEDNESS; WEAK SOLUTIONS; SCHEMES; COUNTEREXAMPLE; CONVERGENCE; GAS;

D O I：

10.1007/978-3-319-49262-9_4

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this note we review and recast some recent results on the existence of non-standard solutions to the compressible Euler equations as to make possible a preliminary numerical investigation. In particular, we are interested in studying numerically the forward in time evolution of some Lipschitz initial data which allow for non-standard solutions ("colliding data"). Numerical results indicate appearance of oscillations after the first break-up time along with a qualitative behavior seemingly compatible with relevant properties of non-standard solutions.

引用

页码：111 / 140

页数：30

共 38 条

[1]

Acharya A., 2016, ARXIV160503058

[2]

[Anonymous], 2015, BCAM SPRINGER BRIEFS

[3] Discrete kinetic schemes for multidimensional systems of conservation laws [J].

Aregba-Driollet, D ;

Natalini, R .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 37 (06) :1973-2004

[4] Vanishing viscosity solutions of nonlinear hyperbolic systems [J].

Bianchini, S ;

Bressan, A .

ANNALS OF MATHEMATICS, 2005, 161 (01) :223-342

[5]

Blondin JM, 1997, NEW ASTRON, V1, P235

[6] A kinetic formulation for multi-branch entropy solutions of scalar conservation laws [J].

Brenier, Y ;

Corrias, L .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1998, 15 (02) :169-190

[7]

Chiodaroli E., 2015, ARXIV151103114

[8] On the weak solutions to the equations of a compressible heat conducting gas [J].

Chiodaroli, Elisabetta ;

Feireisl, Eduard ;

Kreml, Ondrej .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2015, 32 (01) :225-243

[9] Global Ill-Posedness of the Isentropic System of Gas Dynamics [J].

Chiodaroli, Elisabetta ;

De Lellis, Camillo ;

Kreml, Ondrej .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2015, 68 (07) :1157-1190

[10] On the Energy Dissipation Rate of Solutions to the Compressible Isentropic Euler System [J].

Chiodaroli, Elisabetta ;

Kreml, Ondrej .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 214 (03) :1019-1049

← 1 2 3 4 →