Perfectly matched layer absorbing boundary condition for nonlinear two-fluid plasma equations

Sun, Xiaofeng; Jiang, Zhonghe; Hu, Xiwei; Zhuang, G.; Jiang, J.F.; Guo, Wenqiang

doi:10.1016/j.jcp.2015.01.033

Cited by 7 publications

(1 citation statement)

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“…Since its introduction in the seminal paper by Bérenger [18], the Perfectly Matched Layer (PML) approach provides an alternative powerful tool to simulate the numerical solution of PDEs in unbounded domains [1,2,3,9,10,17,19,20,21,24,25,32,43]. Concerning nonlinear PDEs, the PML technique has been applied for example to the nonlinear Schrödinger equations [3,9,10,43], Euler and Navier-Stokes equations [31] or two-fluid plasma equations [40]. Concerning the nonlinear wave equations, Appelö and Kreiss [2] proposed and studied a first-order PML formulation with Dirichlet/Neumann boundary conditions related to Hagstrom techniques [1,29].…”

Section: Introductionmentioning

confidence: 99%

Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes

Antoine,

Zhao

2021

Preprint

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Two different Perfectly Matched Layer (PML) formulations with efficient pseudospectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon equations (NKGE). A pseudo-spectral explicit exponential integrator scheme for a firstorder formulation and a linearly implicit preconditioned finite-difference scheme for a secondorder formulation are proposed and analyzed. To obtain a high spatial accuracy, new regularized Bermúdez type absorption profiles are introduced for the PML. It is shown that the two schemes are efficient, but the linearly implicit scheme should be preferred for accuracy purpose when used within the framework of pseudo-spectral methods combined with the regularized Bermúdez type functions. In addition, in the non-relativistic regime, numerical examples lead to the conclusion that the error related to regularized Bermúdez type absorption functions is insensitive to the small parameter ε involved in the NKGE. The paper ends by a two-dimensional example showing that the strategy extends to the rotating NKGE where the vortex dynamics is very well-reproduced.

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