Compact finite volume schemes on boundary-fitted grids

  • Authors:

  • M. Piller;E. Stalio

  • Affiliations:

  • Dipartimento di Ingegneria Civile ed Ambientale - Sezione Georisorse, Universití degli Studi di Trieste, Via A. Valerio, 6/1, 34127 Trieste, Italy;Dipartimento di Ingegneria Meccanica e Civile, Universití di Modena e Reggio Emilia, Via Vignolese, 905/B, 41100 Modena, MO, Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

The paper focuses on the development of a framework for high-order compact finite volume discretization of the three-dimensional scalar advection-diffusion equation. In order to deal with irregular domains, a coordinate transformation is applied between a curvilinear, non-orthogonal grid in the physical space and the computational space. Advective fluxes are computed by the fifth-order upwind scheme introduced by Pirozzoli [S. Pirozzoli, Conservative hybrid compact-WENO schemes for shock-turbulence interaction, J. Comp. Phys. 178 (2002) 81] while the Coupled Derivative scheme [M.H. Kobayashi, On a class of Pade finite volume methods, J. Comp. Phys. 156 (1999) 137] is used for the discretization of the diffusive fluxes. Numerical tests include unsteady diffusion over a distorted grid, linear free-surface gravity waves in a irregular domain and the advection of a scalar field. The proposed methodology attains high-order formal accuracy and shows very favorable resolution characteristics for the simulation of problems with a wide range of length scales.