A Characteristic Mapping Method for the two-dimensional incompressible Euler equations

Abstract

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 gradient-augmented 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.

arXiv comment32 pages

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Cited by in corpus (8)

• A Characteristic Mapping Method for the three-dimensional incompressible Euler equations
• An Eulerian Vortex Method on Flow Maps
• A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties
• Fluid Simulation on Vortex Particle Flow Maps
• A Characteristic Mapping Method for Tracer Transport on the Sphere
• Lagrangian Covector Fluid with Free Surface
• Singularity formation of vortex sheets in 2D Euler equations using the characteristic mapping method
• A Characteristic Mapping Method with Source Terms: Applications to Ideal Magnetohydrodynamics