Free Access
Issue
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
Page(s) 713 - 734
DOI https://doi.org/10.1051/m2an/2021009
Published online 05 May 2021
  1. P. Arminjon, M.-C. Viallon and A. Madrane, A finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for conservation laws on unstructured grids. Int. J. Comput. Fluid Dyn. 9 (1997) 1–22. [Google Scholar]
  2. D.S. Balsara and B. Nkonga, Multidimensional Riemann problem with self-similar internal structure – part III – a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems. J. Comput. Phys. 346 (2017) 25–48. [Google Scholar]
  3. J. Cheng and C.-W. Shu, A high order ENO conservative Lagrangian type scheme for the compressible Euler equations. J. Comput. Phys. 227 (2007) 1567–1596. [Google Scholar]
  4. J. Cheng and C.-W. Shu, A third order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equations. Commun. Comput. Phys. 4 (2008) 1008–1024. [Google Scholar]
  5. A. Chertock, S. Cui, A. Kurganov, S.N. Özcan and E. Tadmor, Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes. J. Comput. Phys. 358 (2018) 36–52. [Google Scholar]
  6. D.P. Dempsey and R. Rotunno, Topographic generation of mesoscale vortices in mixed-layer models. J. Atmos. Sci. 45 (1988) 2961–2978. [Google Scholar]
  7. J. Dewar, A. Kurganov and M. Leopold, Pressure-based adaption indicator for compressible Euler equations. Numer. Methods Part. Differ. Equ. 31 (2015) 1844–1874. [Google Scholar]
  8. U.S. Fjordholm, S. Mishra and E. Tadmor, On the computation of measure-valued solutions. Acta Numer. 25 (2016) 567–679. [Google Scholar]
  9. E. Godlewski and P.-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. In: Vol. 118 of Applied Mathematical Sciences. Springer-Verlag, New York (1996). [Google Scholar]
  10. S.K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Mat. Sb. (N.S.) 47 (1959) 271–306. [MathSciNet] [Google Scholar]
  11. S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (2001) 89–112. [Google Scholar]
  12. S. Gottlieb, D. Ketcheson and C.-W. Shu, Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2011). [Google Scholar]
  13. E. Gouzien, N. Lahaye, V. Zeitlin and T. Dubos, Thermal instability in rotating shallow water with horizontal temperature/density gradients. Phys. Fluids 29 (2017) 101702. [Google Scholar]
  14. J.-L. Guermond and B. Popov, Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations. J. Comput. Phys. 321 (2016) 908–926. [Google Scholar]
  15. A. Harten, P. Lax and B. van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35–61. [Google Scholar]
  16. J.S. Hesthaven, Numerical methods for conservation laws. From analysis to algorithms. In: Vol. 18 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2018). [Google Scholar]
  17. G.-S. Jiang and E. Tadmor, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19 (1998) 1892–1917. [Google Scholar]
  18. D. Kröner, Numerical Schemes for Conservation Laws. Wiley-Teubner Series Advances in Numerical Mathematics. John Wiley & Sons Ltd., Chichester (1997). [Google Scholar]
  19. A. Kurganov, Central schemes: a powerful black-box solver for nonlinear hyperbolic PDEs. In: Vol. 17 of Handbook of Numerical Methods for Hyperbolic Problems. Elsevier/North-Holland, Amsterdam (2016) 525–548. [Google Scholar]
  20. A. Kurganov, Finite-volume schemes for shallow-water equations. Acta Numer. 27 (2018) 289–351. [Google Scholar]
  21. A. Kurganov and C.-T. Lin, On the reduction of numerical dissipation in central-upwind schemes. Commun. Comput. Phys. 2 (2007) 141–163. [Google Scholar]
  22. A. Kurganov and G. Petrova, A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems. Numer. Math. 88 (2001) 683–729. [Google Scholar]
  23. A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160 (2000) 241–282. [Google Scholar]
  24. A. Kurganov and E. Tadmor, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers. Numer. Methods Part. Differ. Equ. 18 (2002) 584–608. [Google Scholar]
  25. A. Kurganov, S. Noelle and G. Petrova, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23 (2001) 707–740. [Google Scholar]
  26. A. Kurganov, M. Prugger and T. Wu, Second-order fully discrete central-upwind scheme for two-dimensional hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 39 (2017) A947–A965. [Google Scholar]
  27. A. Kurganov, Y. Liu and V. Zeitlin, Thermal vs isothermal rotating shallow water equations: comparison of dynamical processes in two models by simulations with a novel well-balanced central-upwind scheme. To appear in: Geophys. Astro. Fluid Dyn. (2020) DOI: 10.1080/03091929.2020.1774876. [Google Scholar]
  28. A. Kurganov, Y. Liu and V. Zeitlin, A well-balanced central-upwind scheme for the thermal rotating shallow water equations. J. Comput. Phys. 411 (2020) 109414. [Google Scholar]
  29. R.L. Lavoie, A mesoscale numerical model of lake-effect storms. J. Atmos. Sci. 29 (1972) 1025–1040. [Google Scholar]
  30. P.D. Lax and X.-D. Liu, Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAM J. Sci. Comput. 19 (1998) 319–340 (electronic). [Google Scholar]
  31. R.J. LeVeque, High resolution finite volume methods on arbitrary grids via wave propagation. J. Comput. Phys. 78 (1988) 36–63. [Google Scholar]
  32. R.J. LeVeque, Wave propagation algorithms for multi-dimensional hyperbolic systems. J. Comput. Phys. 131 (1997) 327–353. [Google Scholar]
  33. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2002). [Google Scholar]
  34. D. Levy, G. Puppo and G. Russo, Central WENO schemes for hyperbolic systems of conservation laws. ESAIM: M2AN 33 (1999) 547–571. [CrossRef] [EDP Sciences] [Google Scholar]
  35. D. Levy, G. Puppo and G. Russo, Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22 (2000) 656–672. [Google Scholar]
  36. D. Levy, G. Puppo and G. Russo, A fourth-order central WENO scheme for multidimensional hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 24 (2002) 480–506. [Google Scholar]
  37. K.-A. Lie and S. Noelle, On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. SIAM J. Sci. Comput. 24 (2003) 1157–1174. [Google Scholar]
  38. R. Liska and B. Wendroff, Comparison of several difference schemes on 1D and 2D test problems for the euler equations. SIAM J. Sci. Comput. 25 (2003) 995–1017. [Google Scholar]
  39. W. Liu, J. Cheng and C.-W. Shu, High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations. J. Comput. Phys. 228 (2009) 8872–8891. [Google Scholar]
  40. M. Lukáčová-Medviová, K.W. Morton and G. Warnecke, Finite volume evolution Galerkin methods for hyperbolic systems. SIAM J. Sci. Comput. 26 (2004) 1–30. [Google Scholar]
  41. J.P. McCreary, P.K. Kundu and R.L. Molinari, A numerical investigation of dynamics, thermodynamics and mixed-layer processes in the Indian Ocean. Prog. Oceanog. 31 (1993) 181–244. [Google Scholar]
  42. H. Nessyahu and E. Tadmor, Nonoscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [Google Scholar]
  43. J. Panuelos, J. Wadsley and N. Kevlahan, Low shear diffusion central schemes for particle methods. J. Comput. Phys. 414 (2020). [Google Scholar]
  44. P. Ripa, On improving a one-layer ocean model with thermodynamics. J. Fluid Mech. 303 (1995) 169–201. [Google Scholar]
  45. P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (1981) 357–372. [Google Scholar]
  46. M.L. Salby, Deep circulations under simple classes of stratification. Tellus 41A (1989) 48–65. [Google Scholar]
  47. C.W. Schulz-Rinne, Classification of the Riemann problem for two-dimensional gas dynamics. SIAM J. Math. Anal. 24 (1993) 76–88. [Google Scholar]
  48. C.W. Schulz-Rinne, J.P. Collins and H.M. Glaz, Numerical solution of the Riemann problem for two-dimensional gas dynamics. SIAM J. Sci. Comput. 14 (1993) 1394–1394. [Google Scholar]
  49. J. Shi, Y.-T. Zhang and C.-W. Shu, Resolution of high order WENO schemes for complicated flow structures. J. Comput. Phys. 186 (2003) 690–696. [Google Scholar]
  50. P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21 (1984) 995–1011. [Google Scholar]
  51. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 3rd edition. Springer-Verlag, Berlin, Heidelberg (2009). [Google Scholar]
  52. B. van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32 (1979) 101–136. [Google Scholar]
  53. W.R. Young, The subinertial mixed layer approximation. J. Phys. Oceanogr. 24 (1994) 1812–1826. [Google Scholar]
  54. V. Zeitlin, Geophysical Fluid Dynamics: Understanding (almost) Everything with Rotating Shallow Water Models. Oxford University Press, Oxford (2018). [Google Scholar]
  55. Y. Zheng, Systems of conservation laws: Two-dimensional Riemann Problems. In: Vol. 38 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Boston, Inc., Boston, MA (2001). [Google Scholar]

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