Adaptive Characteristic Mapping Method for the Euler Equations – CM2E

extremely high resolution capabilities of the scheme obtained by decomposing the flow map and appropriate remapping

X.-Y. Yin, K. Schneider and J.-C. Nave.
A Characteristic Mapping Method for the three-dimensional incompressible Euler equations.
J. Comput. Phys., 477, 111876, 2023.

S. Taylor, J.-C. Nave
A characteristic mapping method for incompressible hydrodynamics on a rotating sphere.
arXiv:2302.01205

T. Oujia, K. Matsuda and K. Schneider. Computing differential operators of the particle velocity in moving particle clouds using tessellations. Preprint, 12/2022. arXiv:2212.03580

S. V. Apte, T. Oujia, K. Matsuda, B. Kadoch, X. He and K. Schneider. Clustering of inertial particles in turbulent flow through a porous unit cell. J. Fluid Mech., 937, A9, 2022.

X.-Y. Yin, O. Mercier, B. Yadav, K. Schneider and J.-C. Nave. A Characteristic Mapping Method for the two-dimensional incompressible Euler equations. J. Comput. Phys., 424, 109781, 2021.

Even though computational resources grow rapidly, the extremely fine scales in fluid and plasma turbulence remain beyond reach using existing numerical methods. A combination of computational power and ingenious physical insights is usually needed to go beyond the brute force limit. We propose here to develop a novel numerical method, a fully Adaptive Characteristic Mapping Method (ACMM) for evolving the flow map, which yields exponential resolution in linear time. First results for the 2D incompressible Euler equations show the extremely high resolution capabilities of the scheme. The project consists of 2 parts. Part one is focused on the development of ACMM for 2D systems, including its adaptive version using multiresolution techniques and subsequently its application to 2D Euler flows, passive scalar mixing and magnetic reconnection problems. In the second part, we will extend the method to 3D and investigate the formation of singularities and turbulent dissipation.