Olivier Mercier

Research Scientist - Display Systems Research
Facebook Reality Labs

A Characteristic Mapping Method for the two-dimensional incompressible Euler equations
Journal of Computational Physics, 2021
Xi-Yuan Yin
McGill University
Olivier Mercier
McGill University
Badal Yadav
McGill University
Kai Schneider
Aix-Marseille University
Jean-Christophe Nave
McGill University
We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. The new approach evolves the flow map using the gradientaugmented level set method (GALSM). Since the flow map can be decomposed into submaps (each over a finite time interval), the error can be controlled by choosing the remapping times appropriately. This leads to a numerical scheme that has exponential resolution in linear time. Error estimates are provided and conservation properties are analyzed. The computational efficiency and the high precision of the method are illustrated for a vortex merger and a four mode and a random flow. Comparisons with a Cauchy-Lagrangian method are also presented.
  title ={A Characteristic Mapping method for the two-dimensional incompressible Euler equations},
  author = {Yin, Xi-Yuan and Mercier, Olivier and Yadav, Badal and Schneider, Kai and Nave, Jean-Christophe},
  journal = {Journal of Computational Physics},
  volume = {424},
  pages = {109781},
  year = {2021}