Abstract
Abstract We consider the multigrid solution of the transverse circulation equation for a tropical cyclone. First we develop a standard multigrid scheme (SMG) which cycles between different levels of discretization (grids) to efficiently reduce the error in the solution on all scales. Whereas relaxation is inefficient as a solution method, it is used within the multigrid approach as a smoother to reduce the high-wavenumber errors on each grid. The added cost of the coarse grids is small because they contain relatively few points. The efficiency of the SMG scheme is compared to more conventional methods. Gauss-Seidel and successive-over-relaxation (SOR). Results show that the SMG scheme solves to the level of truncation error 26 times faster than an optimal SOR method. In the SMG scheme an unbounded domain is approximated with a wall at a finite radius which leads to significant errors in the numerical solution. To better simulate an unbounded domain, we develop a second scheme (LRMG) which naturally combin...
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