Los Alamos National Lab, EES-2
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As part of an ongoing research project at Los Alamos, a fully implicit fluid dynamics solver capable of simulating such highly nonlinear phenomena as hurricanes or wildfires is currently being developed. Unlike traditional atmospheric science codes that split both dynamical and physical processes from each other, the new solver combines all these processes into effectively one large matrix and then, through the Newton-Krylov machinery, inverts the large matrix. The key to solving this large implicit equation set efficiently is the development of a robust preconditioner. A robust "physics-based'' preconditioner has in fact been developed and was found to reduce computational effort by a factor of 10. The new solver was also found to be more accurate than traditional split approaches with the old approaches having to take a time step at least a 100 times smaller to get the same measure of temporal error as produced by the new solver. An interesting aspect of solving an entire nonlinear system using Newton's method is that physical parameterizations should be formulated such that Newton's method will converge and/or produce a solution that will converge as the time step goes to zero. For example, the typical bulk condensation model used in most weather predictions codes does not include a time scale in its formulation. Regardless of the time step used, if saturation occurs, then a certain fixed amount of condensate is formed. This type of parameterization prevents the solution from converging in time and calls into question the ability of weather prediction models to accurately predict the movement and intensification of storm systems such as hurricanes. Obviously, parameterizations such as condensation will need to be "reworked" to fit within the Newton-Krylov machinery. Even though this "reworking'' of parameterizations is still a work in progress and potentially could take several years to complete, the parameterizations have been smoothed enough to allow for a fully implicit simulation of hurricane. Preliminary results from these hurricane simulations and a description of the Newton-Krylov machinery required to complete these simulations will be presented during the talk. |