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.

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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)