In this paper we consider Runge-Kutta discontinuous Galerkin (RKDG) schemes for Vlasov-Poisson systems that model collisionless plasmas. One-dimensional systems are emphasized. The RKDG method, originally devised to solve conservation laws, is seen to have excellent conservation properties, be readily designed for arbitrary order of accuracy, and capable of being used with a positivity-preservi...

In this paper, we develop and present an arbitrary high order well-balanced finite volume WENO method combined with the modified Patankar Deferred Correction (mPDeC) time integration for shallow water equations. Due to positivity-preserving property of mPDeC, resulting scheme is unconditionally positivity preserving height. To apply mPDeC approach, have interpret spatial semi-discretization in ...

This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for shallow water equations under arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The WENO reconstruction is adopted on moving meshes, which distinguishes smooth, non-smooth, and transition stencils by a simple smoothness detector. To maintain positivi...

In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and local discrete minimum entropy principle, resulting approach can robustly resolve strong discontinuities with sub-element resolution, does not require problem-dependent parameter tuning, ...