A Monge-Ampère enhancement for semi-Lagrangian methods |
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Authors: | Jean-Fran ois Cossette,Piotr K. Smolarkiewicz |
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Affiliation: | a Département de Physique, Université de Montréal, C.P. 6128, Succ. Centre-ville Montréal (Québec) H3C 3J7, Canada;b National Center for Atmospheric Research, Boulder, CO 80307, USA |
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Abstract: | Demanding the compatibility of semi-Lagrangian trajectory schemes with the fundamental Euler expansion formula leads to the Monge-Ampère (MA) nonlinear second-order partial differential equation. Given standard estimates of the departure points of flow trajectories, solving the associated MA problem provides a corrected solution satisfying a discrete Lagrangian form of the mass continuity equation to round-off error. The impact of the MA enhancement is discussed in two diverse limits of fluid dynamics applications: passive tracer advection in a steady cellular flow and in fully developed turbulence. Improvements of the overall accuracy of simulations depend on the problem and can be substantial. |
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Keywords: | Semi-Lagrangian approximations Monge-Ampè re equations Non-linear elliptic equations Incompressible turbulent flows |
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