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A second order well-balanced finite volume scheme for Euler equations with gravity. (English) Zbl 1320.76078

76M12 Finite volume methods applied to problems in fluid mechanics
65N08 Finite volume methods for boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35Q31 Euler equations
76N15 Gas dynamics (general theory)
Full Text: DOI
[1] C. Berthon, V. Desveaux, C. Klingenberg, and M. Zenk, Well balanced schemes to capture non-explicit steady states. Part 2: Euler with gravity, submitted. · Zbl 1382.65310
[2] C. Berthon, V. Desveaux, C. Klingenberg, and M. Zenk, A well-balanced scheme for the Euler equation with a gravitational potential, in Finite Volumes for Complex Applications. VII. Methods and Theoretical Aspects, Springer Proc. Math. Stat. 77, Springer, Cham, Switzerland, 2014, pp. 217–226. · Zbl 1304.76027
[3] F. G. Fuchs, A. D. 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
[4] H. Guillard and C. Viozat, On the behavior of upwind schemes in the low mach number limit, Comput. Fluids, 28 (1999), pp. 63–96. · Zbl 0963.76062
[5] F. Ismail and P. L. Roe, Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks, J. Comput. Phys., 228 (2009), pp. 5410–5436. · Zbl 1280.76015
[6] R. Käppeli and S. Mishra, Well-balanced schemes for the Euler equations with gravitation, J. Comput. Phys., 259 (2014), pp. 199–219. · Zbl 1349.76345
[7] L. D. Landau and E. M. Lifschitz, Fluid Mechanics, 2nd ed., Course of Theoretical Physics, Butterworth-Heinemann, Oxford, 1987.
[8] 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
[9] R. J. LeVeque and D. S. Bale, Wave propagation methods for conservation laws with source terms, in Hyperbolic Problems: Theory, Numerics, Applications, R. Jeltsch and M. Fey, eds., Internat. Ser. Numer. Math. 130, Birkhäuser, Basel, 1999, pp. 609–618. · Zbl 0927.35062
[10] 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
[11] P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 43 (1981), pp. 357–372. · Zbl 0474.65066
[12] C.-W. Shu and S. Osher, Efficient implementation of essentially nonoscillatory shock-capturing schemes, J. Comput. Phys., 77 (1988), pp. 439–471. · Zbl 0653.65072
[13] E. F. Toro, M. Spruce, and W. Speares, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, 4 (1994), pp. 25–34. · Zbl 0811.76053
[14] R. Touma, U. Koley, and C. Klingenberg, Well-balanced unstaggered central scheme for the Euler equation with gravity, submitted. · Zbl 1346.76100
[15] 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
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