Zooming into Kinetic Equations using the Characteristic Mapping Method
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Our work introduces an efficient semi-Lagrangian characteristic mapping method for solving kinetic equations with high precision on coarse grids. Its ability is demonstrated for the one+one-dimensional Vlasov–Poisson equation. This method employs a numerically evolved flow map utilizing a gradient-augmented level-set technique, achieving exponential resolution within linear time. We demonstrate the method’s global third-order convergence in space and time while rigorously evaluating its conservation properties. Benchmarking against established test cases such as Landau damping and the two-stream instability showcases the effectiveness of our approach, highlighting its superiority over classical pseudo-spectral methods. Moreover, we illustrate the method’s exceptional capability to transcend the limits of currently available schemes by showcasing its extreme fine-scale resolution features. Our method stands as a promising advancement in addressing the computational challenges associated with kinetic theories, offering a pathway towards unprecedented precision in simulations.
