Abstract
We present numerical simulations of a model of coupling between a inviscid compressible fluid and a pointwise particle. The particle is seen as a moving interface, through which interface conditions are prescribed. Key points are to impose those conditions at the numerical level, and to deal with the coupling between an ordinary and a partial differential equations.
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References
Abgrall, R., Karni, S.: Computations of compressible multifluids. J. Comput. Phys. 169(2), 594–623 (2001)
Aguillon, N.: Riemann problem for a fluid-particule coupling (2014) (Submitted)
Andreianov, B., Karlsen, K.H., Risebro, N.H.: A study of \(L^1\)-dissipative solvers for scalar conservation laws with discontinuous flux. Arch. Ration. Mech. Anal. 201, 27–86 (2011)
Andreianov, B., Lagoutière, F., Seguin, N., Takahashi, T.: Well-posedness for a one-dimensional fluid-particle interaction model. SIAM J. Math. Appl. 46(2), 1030–1052 (2014)
Andreianov, B., Seguin, N.: Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes. Discrete Contin. Dyn. Syst. 32,1939–1964 (2012)
Borsche, R., Colombo, R.M., Garavello, M.: On the interactions between a solid body and a compressible inviscid fluid. To appear in Interfaces Free Bound (2014)
Boutin, B., Coquel, F., LeFloch, P.G.: Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces. SIAM J. Numer. Anal. 51, 1108–1133 (2013)
Colombo, R.M., Guerra, G.: On general balance laws with boundary. J. Diff. Equat. 1017–1043 (2010)
Dal Maso, G., Lefloch, P.G., Murat, F.: Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74(6), 483–548 (1995)
Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152, 457–492 (1999)
Goatin, P., LeFloch, P.G.: The Riemann problem for a class of resonant hyperbolic systems of balance laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 21, 881–902 (2004)
Greenberg, J.M., Leroux, A.Y.: A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33(1), 1–16 (1996)
Hayes, B.T., Lefloch, P.G.: Nonclassical shocks and kinetic relations: strictly hyperbolic systems. SIAM J. Math. Anal. 31(5), 941–991 (2000)
Isaacson, E., Temple, B.: Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. 52, 1260–1278 (1992)
Lagoutière, F., Seguin, N., Takahashi, T.: A simple 1D model of inviscid fluid-solid interaction. J. Diff. Equat. 245, 3503–3544 (2008)
Parés, C.: Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J. Numer. Anal. 44, 300–321 (2006)
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Aguillon, N. (2014). Numerical Simulations of a Fluid-Particle Coupling. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_76
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DOI: https://doi.org/10.1007/978-3-319-05591-6_76
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