Institute for Mathematics Applied to Geosciences (IMAGe)

Geophysical and Astrophysical Spectral element Adaptive Refinement (GASpAR) code

GASpAR Team: Duane Rosenberg, Aimé Fournier, Annick Pouquet

GASpAR ( Download here ) is an object-oriented geophysical and astrophysical spectral-element adaptive refinement code. 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 multi-scale problems arise. The formalism accommodates both conforming and non-conforming elements. GASpAR includes a new formulation of dynamic adaptive refinement (DARe) of non-conforming h-type. As a demonstration of the code, several new 2D test cases have been introduced and performed 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 have been tabulated for 2D spatial and temporal convergence of DARe.

Accurate and efficient simulation of strongly turbulent flows is a prevalent challenge in many atmospheric, oceanic, and astrophysical applications. New simulation codes are needed to investigate such flows in the parameter regimes that interest the geophysics communities. Turbulent flows are linked to many issues in the geosciences, for example, in meteorology, oceanography, climatology, ecology, solar-terrestrial interactions, and solar fusion, as well as dynamo effects, specifically, magnetic-field generation in cosmic bodies by turbulent motions. Nonlinearities prevail when the Reynolds number Re is large. The number of degrees of freedom in three dimensions increases as Re9/4 as Re tends to infinity in the Kolmogorov 1941 framework. For aeronautic flows often Re>106, but for geophysical flows often Re>>108. Also, computations of turbulent flows must contain enough scales to encompass the energy-containing and dissipative scale ranges distinctly. Uniform-grid convergence studies on 3D compressible-flow simulations show that in order to achieve the desired scale content, uniform grids must contain at least 20483 cells. Today such computations can barely be accomplished. A pseudo-spectral Navier-Stokes code on a grid of 40963 uniformly spaced points has been run on the Earth Simulator, but the Taylor Reynolds number (proportional to Re1/2) is still no more than about 700, very far from what is required for most geophysical flows. The main goal of the present code development is to ask, if the significant structures of the flow are indeed sparse, so that their dynamics can be followed accurately even if they are embedded in random noise, then does dynamic adaptivity offer a means for achieving otherwise unattainable large Re values. Thus, we have developed GASpAR for simulating and studying turbulent phenomena.

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Last modified: Wednesday, 21-Oct-2009 11:13:05 MDT