A higher order Finite Volume resolution method for a system related to the inviscid primitive equations in a complex domain

Abstract

We construct the cell-centered Finite Volume discretization of the two-dimensional inviscid primitive equations in a domain with topography. To compute the numerical fluxes, the so-called Upwind Scheme (US) and the Central-Upwind Scheme (CUS) are introduced. For the time discretization, we use the classical fourth order Runge–Kutta method. We verify, with our numerical simulations, that the US (or CUS) is a robust first (or second) order scheme, regardless of the shape or size of the topography and without any mesh refinement near the topography.

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Acknowledgments

This work was supported in part by NSF Grants DMS 1206438 and DMS 1212141, and by the Research Fund of Indiana University. The authors would like to thank Professor Roger Temam and Dr. Joseph Tribbia for their suggestion and advice.

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Correspondence to Gung-Min Gie.

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Bousquet, A., Gie, GM., Hong, Y. et al. A higher order Finite Volume resolution method for a system related to the inviscid primitive equations in a complex domain. Numer. Math. 128, 431–461 (2014). https://doi.org/10.1007/s00211-014-0622-4

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Mathematics Subject Classifications (1991)

  • 65M08
  • 86A10
  • 76B70
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