September  2006, 6(5): 979-1000. doi: 10.3934/dcdsb.2006.6.979

Lagrangian averaging for the 1D compressible Euler equations

1. 

Applied Physics and Applied Mathematics, Columbia University, New York NY 10027, United States

2. 

Department of Mathematics, Stanford University, Stanford CA 94305-2125, United States

Received  June 2005 Revised  March 2006 Published  June 2006

We consider a $1$-dimensional Lagrangian averaged model for an inviscid compressible fluid. As previously introduced in the literature, such equations are designed to model the effect of fluctuations upon the mean flow in compressible fluids. This paper presents a traveling wave analysis and a numerical study for such a model. The discussion is centered around two issues. One relates to the intriguing wave motions supported by this model. The other is the appropriateness of using Lagrangian-averaged models for compressible flow to approximate shock wave solutions of the compressible Euler equations.
Citation: Harish S. Bhat, Razvan C. Fetecau. Lagrangian averaging for the 1D compressible Euler equations. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 979-1000. doi: 10.3934/dcdsb.2006.6.979
[1]

Paolo Secchi. An alpha model for compressible fluids. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 351-359. doi: 10.3934/dcdss.2010.3.351

[2]

Alberto Bressan. Impulsive control of Lagrangian systems and locomotion in fluids. Discrete and Continuous Dynamical Systems, 2008, 20 (1) : 1-35. doi: 10.3934/dcds.2008.20.1

[3]

Anna Abbatiello, Eduard Feireisl, Antoní Novotný. Generalized solutions to models of compressible viscous fluids. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 1-28. doi: 10.3934/dcds.2020345

[4]

Eugenio Aulisa, Lidia Bloshanskaya, Akif Ibragimov. Well productivity index for compressible fluids and gases. Evolution Equations and Control Theory, 2016, 5 (1) : 1-36. doi: 10.3934/eect.2016.5.1

[5]

Eduard Feireisl, Antonín Novotný. Two phase flows of compressible viscous fluids. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022091

[6]

Van-Sang Ngo, Stefano Scrobogna. Dispersive effects of weakly compressible and fast rotating inviscid fluids. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 749-789. doi: 10.3934/dcds.2018033

[7]

Eduard Feireisl. On weak solutions to a diffuse interface model of a binary mixture of compressible fluids. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 173-183. doi: 10.3934/dcdss.2016.9.173

[8]

Konstantina Trivisa. Global existence and asymptotic analysis of solutions to a model for the dynamic combustion of compressible fluids. Conference Publications, 2003, 2003 (Special) : 852-863. doi: 10.3934/proc.2003.2003.852

[9]

Werner Bauer, François Gay-Balmaz. Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations. Journal of Computational Dynamics, 2019, 6 (1) : 1-37. doi: 10.3934/jcd.2019001

[10]

Mauro Fabrizio, Claudio Giorgi, Angelo Morro. Phase transition and separation in compressible Cahn-Hilliard fluids. Discrete and Continuous Dynamical Systems - B, 2014, 19 (1) : 73-88. doi: 10.3934/dcdsb.2014.19.73

[11]

Lvqiao liu, Lan Zhang. Optimal decay to the non-isentropic compressible micropolar fluids. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4575-4598. doi: 10.3934/cpaa.2020207

[12]

Haigang Li, Jiguang Bao. Euler-Poisson equations related to general compressible rotating fluids. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1085-1096. doi: 10.3934/dcds.2011.29.1085

[13]

Paola Goatin, Philippe G. LeFloch. $L^1$ continuous dependence for the Euler equations of compressible fluids dynamics. Communications on Pure and Applied Analysis, 2003, 2 (1) : 107-137. doi: 10.3934/cpaa.2003.2.107

[14]

Bernard Ducomet, Eduard Feireisl, Hana Petzeltová, Ivan Straškraba. Global in time weak solutions for compressible barotropic self-gravitating fluids. Discrete and Continuous Dynamical Systems, 2004, 11 (1) : 113-130. doi: 10.3934/dcds.2004.11.113

[15]

Colette Guillopé, Zaynab Salloum, Raafat Talhouk. Regular flows of weakly compressible viscoelastic fluids and the incompressible limit. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1001-1028. doi: 10.3934/dcdsb.2010.14.1001

[16]

Hyeong-Ohk Bae, Young-Pil Choi, Seung-Yeal Ha, Moon-Jin Kang. Asymptotic flocking dynamics of Cucker-Smale particles immersed in compressible fluids. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4419-4458. doi: 10.3934/dcds.2014.34.4419

[17]

Tomáš Roubíček. From quasi-incompressible to semi-compressible fluids. Discrete and Continuous Dynamical Systems - S, 2021, 14 (11) : 4069-4092. doi: 10.3934/dcdss.2020414

[18]

T. Tachim Medjo. Averaging of a 3D Lagrangian averaged Navier-Stokes-$\alpha$ model with oscillating external forces. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1281-1305. doi: 10.3934/cpaa.2011.10.1281

[19]

Matthias Hieber, Miho Murata. The $L^p$-approach to the fluid-rigid body interaction problem for compressible fluids. Evolution Equations and Control Theory, 2015, 4 (1) : 69-87. doi: 10.3934/eect.2015.4.69

[20]

Ansgar Jüngel, Josipa-Pina Milišić. Full compressible Navier-Stokes equations for quantum fluids: Derivation and numerical solution. Kinetic and Related Models, 2011, 4 (3) : 785-807. doi: 10.3934/krm.2011.4.785

2020 Impact Factor: 1.327

Metrics

  • PDF downloads (138)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]