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Well-balanced unstaggered central schemes for the Euler equations with gravitation. (English) Zbl 1346.76100

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35Q31 Euler equations
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[1] E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein, and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comput., 25 (2004), pp. 2050–2065. · Zbl 1133.65308
[2] N. Botta, S. Langenberg, R. Klein, and S. Lützenkirchen, Well balanced finite volume methods for nearly hydrostatic flows, J. Comput. Phys., 196 (2004), pp. 539–565. · Zbl 1109.86304
[3] M. Castro, J. M. Gallardo, and C. Parés, High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems, Math. Comp., 75 (2006), pp. 1103–1134. · Zbl 1096.65082
[4] N. Črnjarić-Žic, S. Vuković, and L. Sopta, Balanced central NT schemes for the shallow water equations, in Proceedings of the Conference on Applied Mathematics and Scientific Computing, Springer, Dordrecht, the Netherlands, 2005, pp. 171–185.
[5] V. Desveaux, M. Zenk, C. Berthon, and C. Klingenberg, A well-balanced scheme to capture non-explicit steady states in the Euler equations with gravity, Internat. J. Numer. Methods Fluids, 81 (2016), pp. 104–127. · Zbl 1382.65310
[6] F. Fuchs, A. McMurry, S. Mishra, N. H. Risebro, and K. Waagan, High order well-balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres, J. Comput. Phys., 229 (2010), pp. 4033–4058. · Zbl 1190.76153
[7] H. T. Janka, K. Langanke, A. Marek, G. Martínez-Pinedo, and B. Müller, Theory of core-collapse supernovae, Phys. Rep., 442 (2007), pp. 38–74.
[8] R. Käppeli and S. Mishra, Well-balanced schemes for the Euler equations with gravitation, J. Comput. Physics., 259 (2014), pp. 199–219. · Zbl 1349.76345
[9] D. Kröner and M. D. Thanh, Numerical solutions to compressible flows in a nozzle with variable cross-section, SIAM J. Numer. Anal., 43 (2005), pp. 796–824. · Zbl 1093.35050
[10] P. G. Lefloch and M. D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section, Commun. Math. Sci, 1 (2003), pp. 763–797. · Zbl 1091.35044
[11] R. J. LeVeque, A well-balanced path-integral f-wave method for hyperbolic problems with source terms, J. Sci. Comput., 48 (2011), pp. 209–226. · Zbl 1221.65233
[12] R. J. LeVeque, Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm, J. Comput. Phys., 146 (1998), pp. 346–365. · Zbl 0931.76059
[13] R. J. LeVeque and D. S. Bale, Wave propagation methods for conservation laws with source terms, in Proceedings of the 7th International Conferences on Hyperbolic Problems, 1998, Birkhäuser, Basel, 1999, pp. 609–618. · Zbl 0927.35062
[14] H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408–463. · Zbl 0697.65068
[15] S. Noelle, Y. Xing, and C.-W. Shu, High-order well-balanced finite volume WENO schemes for shallow water equation with moving water, J. Comput. Phys., 226 (2007), pp. 29–58. · Zbl 1120.76046
[16] Y. Xing and C.-W. Shu, High order well-balanced WENO scheme for the gas dynamics equations under gravitational fields, J. Sci. Comput., 54 (2013), pp. 645–662. · Zbl 1260.76022
[17] J. G. Zhou, D. M. Causon, C. G. Mingham, and D. M. Ingram, The surface gradient method for the treatment of source terms in the shallow water equations, J. Comput. Phys., 168 (2001), pp. 1–25. · Zbl 1074.86500
[18] J. Luo, K. Xu, and N. Liu, A well-balanced symplecticity-preserving gas-kinetic scheme for hydrodynamic equations under gravitational field, SIAM J. Sci. Comput., 33 (2011), pp. 2356–2381. · Zbl 1232.76044
[19] C. T. Tian, K. Xu, K. L. Chan, and L. C. Deng, A three-dimensional multidimensional gas-kinetic scheme for the Navier-Stokes equations under gravitational fields, J. Comput. Phys., 226 (2007), pp. 2003–2027. · Zbl 1388.76313
[20] G. Li and Y. Xing, High order finite volume WENO schemes for the Euler equations under gravitational fields, J. Comput. Phys., 316 (2016), pp. 145–163. · Zbl 1349.76356
[21] R. Touma and S. Khankan, Well-balanced unstaggered central schemes for one and two-dimensional shallow water equation systems, Appl. Math. Comput., 218 (2012), pp. 5948–5960. · Zbl 1426.76433
[22] R. Touma and C. Klingenberg, Well-balanced central finite volume methods for the Ripa system, Appl. Numer. Math., 2015, pp. 42–68. · Zbl 1329.76217
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