Geophysical-astrophysical spectral-element adaptive refinement (GASpAR): Object-oriented h-adaptive code for geophysical fluid dynamics simulation

We present an object-oriented geophysical and astrophysical spectral-element adaptive refinement (GASpAR) code for application to turbulent flows. Like most spectralelement 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. For extensibility and flexibilty the code is designed in an object-oriented manner. The computational core is based on spectral-element operators, which are represented as objects. The formalism accommodates both conforming and nonPreprint submitted to J. Comp. Phys. 11 May 2005 conforming elements and their associated data structures for handling interelement communications in a parallel environment. Many aspects of this code are a synthesis of existing methods; however, we focus on a new formulation of dynamic adaptive refinement (DARe) of nonconforming h-type. This paper presents the code and its algorithms; we do not consider parallel efficiency metrics or performance. As a demonstration of the code we offer several two-dimensional test cases that we propose as standard test problems for comparable DARe codes. The suitability of these test problems for turbulent flow simulation is considered.