Multigrid Methods for Atmospheric Flow Problems

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The wide range of space and time scales of atmospheric motions poses a fundamental challenge in numerical weather prediction and modeling. Not only is there spatial differences in phenomena such as fronts and cyclones, but also in the types of wave motions which occur. Solving the equations of motion efficiently and in a way that avoids the development of spurious solutions is quite complex. The overall goal of this research is to investigate the potential application of multigrid methods to atmospheric models as a means of overcoming some of these difficulties. The study will concentrate on two main areas. First, the principal investigator will extend his current results on fast multigrid solvers for nonlinear elliptic problems by developing a multigrid solver for the semigeostrophic invertibility relation in three dimensions. The coupling of the multigrid processing with adaptive mesh refinement based on the estimated local truncation error will also be studied in this model. Second, multigrid acceleration of semi-implicit time differencing in primitive equation models will be investigated.