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The property of Semi-Lagrangian Schemes to remove the CFL condition in hyperbolic PDEs has led these schemes to successful applications in Plasma Physics. However, standard semi-Lagrangian methods primarily introduce numerical diffusion due to interpolation and pose challenges in parallelization, especially when employing global interpolation schemes. An alternative formulation of Semi-Lagrangian methods was proposed by Ritchie in 1986, introducing Non-Interpolating Semi-Lagrangian methods for meteorological models. This work has expanded upon Ritchie's formulation, developing numerical schemes for plasma modeling.
Starting with a Vlasov-Poisson model, it has been possible to perform simulations with high CFL values while maintaining the validity of the physics in classical experiments, such as Landau damping.
The study ends with the application of NISL to the Plasma Sheath Formation model. This achievement is reached by using RK integrators and WENO (Weighted Essentially Non-Oscillatory) discretization techniques. This method proves particularly effective for simulating Sheath Formation in plasma, a task complicated by strong gradients due to the diverging electric field, which challenge many numerical solvers.