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 Burger's 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. (c) 2005 Elsevier Inc. All rights reserved.