A high order time splitting method based on integral deferred correction for semi-Lagrangian Vlasov simulations

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• 作者：Andrew Christlieb^a ; ¹ ; ^{andrewch@math.msu.edu" class="auth_mail} ; Wei Guo^b ; ² ; ^{wguo126@math.uh.edu" class="auth_mail} ; Maureen Morton^c ; ^{mmorton@starkstate.edu" class="auth_mail} ; Jing-Mei Qiu^b ; ² ; ^{jingqiu@math.uh.edu" class="auth_mail}
• 关键词：Vlasov&ndash ; Poisson system ; Guiding center model ; Operator/dimensional splitting ; Semi-Lagrangian method ; WENO reconstruction ; Integral deferred correction
• 刊名：Journal of Computational Physics
• 出版年：15 June, 2014
• 年：2014
• 卷：267
• 期：Complete
• 页码：7-27
• 全文大小：3683 K

文摘

Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in Qiu and Christlieb (2010) is very high (as high as ninth order). However, the temporal error is dominated by the operator splitting error, which is second order for Strang splitting. It is therefore important to overcome such low order splitting error, in order to have numerical algorithms that achieve higher orders of accuracy in both space and time. In this paper, we propose to use the integral deferred correction (IDC) method to reduce the splitting error. Specifically, the temporal order accuracy is increased by r with each correction loop in the IDC framework, where for coupling the first order splitting and the Strang splitting, respectively. The proposed algorithm is applied to the Vlasov-Poisson system, the guiding center model, and two dimensional incompressible flow simulations in the vorticity stream-function formulation. We show numerically that the IDC procedure can automatically increase the order of accuracy in time. We also investigate numerical stability of the proposed algorithm via performing Fourier analysis to a linear model problem.