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A Monge-Ampère enhancement for semi-Lagrangian methods

✍ Scribed by Jean-François Cossette; Piotr K. Smolarkiewicz

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
924 KB
Volume
46
Category
Article
ISSN
0045-7930

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

A symmetrization result for Monge–Ampère
A symmetrization result for Monge–Ampère type equations
✍ Barbara Brandolini; Cristina Trombetti 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 171 KB

## Abstract In this paper we prove some comparison results for Monge–Ampère type equations in dimension two. We also consider the case of eigenfunctions and we derive a kind of “reverse” inequalities. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)