A Monge-Ampère enhancement for semi-Lagrangian methods

A Monge-Ampère enhancement for semi-Lagrangian methods

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...

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Veröffentlicht in:Computers & fluids 2011-07, Vol.46 (1), p.180-185
Hauptverfasser: Cossette, Jean-François, Smolarkiewicz, Piotr K.
Format: Artikel
Sprache:eng
Schlagworte:
Cellular
Computational fluid dynamics
Computer simulation
Fluid flow
Incompressible turbulent flows
Mathematical models
Monge-Ampère equations
Non-linear elliptic equations
Semi-Lagrangian approximations
Trajectories
Turbulence
Turbulent flow
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creator Cossette, Jean-François
Smolarkiewicz, Piotr K.
description 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.
doi_str_mv 10.1016/j.compfluid.2011.01.029
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subjects Cellular
Computational fluid dynamics
Computer simulation
Fluid flow
Incompressible turbulent flows
Mathematical models
Monge-Ampère equations
Non-linear elliptic equations
Semi-Lagrangian approximations
Trajectories
Turbulence
Turbulent flow
title A Monge-Ampère enhancement for semi-Lagrangian methods
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