This paper deals with the non-conservative coupling of two one-dimensional barotropic Euler systems at an interface at x = 0. The closure pressure laws differ in the domains x < 0 and x > 0, and a Dirac source term concentrated at x = 0 models singular pressure losses. We propose two numerical methods. The first one relies on ghost state reconstructions at the interface while the second is based on a suitable relaxation framework. Both methods satisfy a well-balanced property for stationary solutions. In addition, the second method preserves mass conservation and exactly restores the prescribed singular pressure drops for both unsteady and steady solutions.
Mots-clés : gas dynamics equations, interfacial coupling, measure valued load, relaxation method, coupled Riemann problem
@article{M2AN_2014__48_3_895_0,
author = {Ambroso, Annalisa and Chalons, Christophe and Coquel, Fr\'ed\'eric and Gali\'e, Thomas},
title = {Interface model coupling \protect\emph{via }prescribed local flux balance},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {895--918},
publisher = {EDP-Sciences},
volume = {48},
number = {3},
year = {2014},
doi = {10.1051/m2an/2013125},
zbl = {1292.35166},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2013125/}
}
TY - JOUR AU - Ambroso, Annalisa AU - Chalons, Christophe AU - Coquel, Frédéric AU - Galié, Thomas TI - Interface model coupling via prescribed local flux balance JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 895 EP - 918 VL - 48 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013125/ DO - 10.1051/m2an/2013125 LA - en ID - M2AN_2014__48_3_895_0 ER -
%0 Journal Article %A Ambroso, Annalisa %A Chalons, Christophe %A Coquel, Frédéric %A Galié, Thomas %T Interface model coupling via prescribed local flux balance %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 895-918 %V 48 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013125/ %R 10.1051/m2an/2013125 %G en %F M2AN_2014__48_3_895_0
Ambroso, Annalisa; Chalons, Christophe; Coquel, Frédéric; Galié, Thomas. Interface model coupling via prescribed local flux balance. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 3, pp. 895-918. doi : 10.1051/m2an/2013125. http://www.numdam.org/articles/10.1051/m2an/2013125/
[1] and , Optimal entropy solutions for conservation laws with discontinuous flux-functions. J. Hyperbolic Differ. Equ. 2 (2005) 783-837. | MR | Zbl
[2] , , , Godunov-type approximation for a general resonant balance law with large data. J. Differ. Equ. 198 (2004) 233-274. | MR | Zbl
[3] , , , , , and , The coupling of homogeneous models for two-phase flows. Int. J. Finite Volumes 4 (2007) 1-39. | MR
[4] , , , , , and , Coupling of general Lagrangian systems. Math. Comput. 77 (2008) 909-941. | MR | Zbl
[5] , and , A method to couple HEM and HRM two-phase flow models. Comput. Fluids 38 (2009) 738-756. | MR | Zbl
[6] and , Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies. Proc. Roy. Soc. Edinburgh Sect. A 135 (2005) 253-265. | MR | Zbl
[7] and , Existence and uniqueness of entropy solution of scalar conservation laws with a flux function involving discontinuous coefficients. Commun. Partial Differential Equations 31 (2006) 371-395. | MR | Zbl
[8] , , , , , , , , , Neptune: a new software platform for advanced nuclear thermal hydraulics. Nuclear Science and Engineering 156 (2007) 281-324.
[9] , Nonlinear stability of Finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources. Frontiers in Mathematics, Birkhauser (2004). | MR | Zbl
[10] , and , Existence result for the coupling problem of two scalar conservation laws with Riemann initial data. Math. Models Methods Appl. Sci. 20 (2010) 1859-1898. | MR | Zbl
[11] , and , Coupling techniques for nonlinear hyperbolic equations. I. Self-similar diffusion for thin interfaces. Proc. Roy. Soc. Edinburgh Sect. A 141 (2011) 921-956. | MR | Zbl
[12] and , Analysis of the NUPEC PSBT Tests with FLICA-OVAP. Science and Technology of Nuclear Installations. Article ID 2012 (2012) 436142.
[13] and , Conservation laws with discontinuous flux: a short introduction. J. Engrg. Math. 60 (2008) 241-247. | MR | Zbl
[14] , and , An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. SIAM J. Numer. Anal. 47 (2009) 1684-1712. | MR | Zbl
[15] , and , The interface coupling of the gas dynamics equations. Quaterly of Applied Mathematics 66 (2008) 659-705. | MR | Zbl
[16] , Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method. Arch. Rational Mech. Anal. 52 (1973) 1-9. | MR | Zbl
[17] , On scalar conservation laws with point source and discontinuous flux function. SIAM J. Math. Anal. 26 (1995) 1425-1451. | MR | Zbl
[18] , Scalar conservation laws with discontinuous flux function. I. The viscous profile condition, Commun. Math. Phys. 176 (1996) 23-44. | MR | Zbl
[19] , Wastewater Hydraulics, Theory and Practice. Springer (2010).
[20] , Couplage interfacial de modèles pour la thermoohydraulique des réacteurs, Ph.D. thesis, Université Pierre et Marie Curie Paris 6 (2008).
[21] and , Solution of the Cauchy problem for a conservation law with a discontinuous flux function. SIAM J. Math. Anal. 23 (1992) 635-648. | MR | Zbl
[22] , and , Numerical method for two phase flow with unstable interface. J. Comput. Phys. 39 (1981) 179-200. | MR | Zbl
[23] and , The Riemann problem for a class of resonant hyperbolic systems of balance laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 881-902. | Numdam | MR | Zbl
[24] , and , The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. II. The case of systems. M2AN Math. Model. Numer. Anal. 39 (2005) 649-692. | Numdam | MR | Zbl
[25] and , The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I. The scalar case. Numer. Math. 97 (2004) 81-130. | MR | Zbl
[26] , A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms. Math. Models Methods Appl. Sci. 11 (2001) 339-365. | MR | Zbl
[27] , Localization effects and measure source terms in numerical schemes for balance laws. Math. Comp. 71 (2001) 553-582. | MR | Zbl
[28] and , A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1-16. | MR | Zbl
[29] and , Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. 52 (1992) 1260-1278. | MR | Zbl
[30] , , and , Analysis and approximation of conservation laws with source terms. SIAM J. Numer. Anal. 34 (1997) 1980-2007. | MR | Zbl
[31] , Schemes to couple flows between free and porous medium. Proceedings of AIAA (2005) 2005-4861.
[32] and , Coupling two and one-dimensional models through a thin interface. Proceedings of AIAA (2005) 2005-4718.
[33] and , Boundary conditions for the coupling of two-phase flow models. 18th AIAA CFD conference.
[34] , Memento des pertes de charges. Coefficients de pertes de charges singulières et de pertes de charges par frottement. Collection Direction des Etudes et Recherches d'EDF. Eyrolles [in French] (1986).
[35] and , The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 48 (1995) 235-276. | MR | Zbl
[36] , , and , Modeling of pressure drop in two-phase flow in singular geometries. 6th International Symposium on Multiphase Flow, Heat Mass Transfert and Energy Conservation. Xi'an, China, 11-15 July 2009, Paper No MN-30, 2009.
[37] (Ed.), Discharge Characteristics: IAHR Hydraulic Structures Design Manuals 8. Balkema: Rotterdam (1994).
[38] , First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81 (1970) 228-255. | MR | Zbl
Cité par Sources :
