GASpAR

Geophysical–astrophysical spectral-element adaptive refinement (GASpAR): Object-oriented h-adaptive fluid dynamics simulation. An object-oriented geophysical and astrophysical spectral-element adaptive refinement (GASpAR) code is introduced. Like most spectral-element codes, GASpAR combines finite-element efficiency with spectral-method accuracy. It is also designed to be flexible enough for a range of geophysics and astrophysics applications where turbulence or other complex multiscale problems arise. The formalism accommodates both conforming and non-conforming elements. Several aspects of this code derive from existing methods, but here are synthesized into a new formulation of dynamic adaptive refinement (DARe) of non-conforming h-type. As a demonstration of the code, several new 2D test cases are introduced that have time-dependent analytic solutions and exhibit localized flow features, including the 2D Burgers equation with straight, curved-radial and oblique-colliding fronts. These are proposed as standard test problems for comparable DARe codes. Quantitative errors are reported for 2D spatial and temporal convergence of DARe.


References in zbMATH (referenced in 11 articles )

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  1. Abdi, Daniel S.; Giraldo, Francis X.: Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations (2016)
  2. Hatori, Tomoharu; Ito, Atsushi M.; Nunami, Masanori; Usui, Hideyuki; Miura, Hideaki: Level-by-level artificial viscosity and visualization for MHD simulation with adaptive mesh refinement (2016)
  3. Marras, Simone; Kelly, James F.; Moragues, Margarida; Müller, Andreas; Kopera, Michal A.; Vázquez, Mariano; Giraldo, Francis X.; Houzeaux, Guillaume; Jorba, Oriol: A review of element-based Galerkin methods for numerical weather prediction: finite elements, spectral elements, and discontinuous Galerkin (2016)
  4. Kopera, Michal A.; Giraldo, Francis X.: Mass conservation of the unified continuous and discontinuous element-based Galerkin methods on dynamically adaptive grids with application to atmospheric simulations (2015)
  5. Subich, Christopher J.: A robust moving mesh method for spectral collocation solutions of time-dependent partial differential equations (2015)
  6. Kopera, Michal A.; Giraldo, Francis X.: Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations (2014)
  7. Rubio, G.; Fraysse, F.; De Vicente, J.; Valero, E.: The estimation of truncation error by (\tau)-estimation for Chebyshev spectral collocation method (2013)
  8. Taylor, Mark A.; Fournier, Aimé: A compatible and conservative spectral element method on unstructured grids (2010)
  9. Diamessis, P. J.; Lin, Y. C.; Domaradzki, J. A.: Effective numerical viscosity in spectral multidomain penalty method-based simulations of localized turbulence (2008)
  10. Fournier, Aimé: Exact calculation of Fourier series in nonconforming spectral-element methods (2006)
  11. Rosenberg, Duane; Fournier, Aimé; Fischer, Paul; Pouquet, Annick: Geophysical-astrophysical spectral-element adaptive refinement (GASpAR): object-oriented (h)-adaptive fluid dynamics simulation (2006)