Orateur
Description
We present the conservative cascade semi-Lagrangian (CCSL) method recently developed in [3] for solving Vlasov-type equations. This approach performs multidimensional transport via a sequence of conservative one-dimensional remaps along coordinate directions, using characteristic interpolation to ensure strict mass conservation. Unlike [1,2], which rely on mesh intersection techniques for two-dimensional semi-Lagrangian transport, the cascade remap strategy avoids mesh intersections, offering a simpler and more efficient algorithmic framework. While [3] validated the method on linear advection, guiding-center, and relativistic Vlasov-Maxwell systems, we present here its first application to the drift-kinetic model by incorporating the test case from [1]. Numerical results demonstrate the ability of the cascade method to handle this class of problems with good conservation properties.
Joint work with C. Xu and C. Yang.
References
[1] N. Crouseilles, P. Glanc, S. A. Hirstoaga, E. Madaule, M. Mehrenberger, J. Pétri,
A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence, The European Physical Journal D (2014),
doi:10.1140/epjd/e2014-50180-9
[2] L. Einkemmer, A. Moriggl,
A semi-Lagrangian discontinuous Galerkin method for drift-kinetic simulations on GPUs,
SIAM Journal on Scientific Computing (2024),
doi:10.1137/23M1559658
[3] C. Xu, M. Mehrenberger, C. Yang,
A conservative cascade semi-Lagrangian method for solving the Vlasov equation,
Journal of Computational Physics (2026),
doi:10.1016/j.jcp.2026.114847