High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation

doi:10.1007/s42967-021-00150-5

Abstract

Abstract: In this paper, we present a semi-Lagrangian (SL) method based on a non-polynomial function space for solving the Vlasov equation. We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems. To address issues that arise in phase space models of plasma problems, we develop a weighted essentially non-oscillatory (WENO) scheme using trigonometric polynomials. In particular, the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities. Moreover, to obtain a high-order of accuracy in not only space but also time, it is proposed to apply a high-order splitting scheme in time. We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system. Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions. A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method. In 6D, this would represent a signifcant savings.

Key words: Semi-Lagrangian methods, WENO schemes, High-order splitting methods, Non-polynomial basis, Vlasov equation, Vlasov-Poisson system

CLC Number:

Andrew Christlieb, Matthew Link, Hyoseon Yang, Ruimeng Chang. High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation[J]. Communications on Applied Mathematics and Computation, 2023, 5(1): 116-142.

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