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An Adaptive semi-lagrangian Level-Set method for Convection-Diffusion Equations on Evolving Interfaces

Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1364-1382页

作者： Weidong Shi Jianjun Xu Shi Shu School of Mathematical and Computational Sciences Xiangtan UniversityXiangtanHunan 411105China Chongqing Institute of Green and Intelligent Technology Chinese Academy of SciencesChongqing 400714China

A new semi-lagrangian scheme is proposed to discretize the surface convection-diffusion *** other involved equations including the the levelset convection equation,the re-initialization equation and the extension equation are also solved by S-L *** S-L method removes both the CFL condition and the stiffness caused by the surface Laplacian,allowing larger time step than the Eulerian *** method is extended to the block-structured adaptive *** examples are given to demonstrate the efficiency of the S-L method.

关键词： Convection-diffusion equation semi-lagrangian method level-set method blockstructured adaptive mesh finite difference method

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A Simple Implementation of the semi-lagrangian Level-Set method

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Advances in Applied Mathematics and Mechanics 2017年第1期9卷 104-124页

作者： Weidong Shi Jian-Jun Xu Shi Shu School of Mathematical and Computational Sciences Xiangtan UniversityXiangtanHunan 411105China Chongqing Institute of Green and Intelligent Technology Chinese Academy of SciencesChongqing 400714China

semi-lagrangian(S-L)methods have no CFL stability constraint,and are more stable than the Eulerian *** the literature,the S-L method for the levelset re-initialization equation was complicated,which may be *** the re-initialization procedure is auxiliary,we propose to use the first-order S-L scheme coupled with a projection technique to improve the accuracy at the grid points just adjacent to the *** second-order S-L method is used for evolving the level-set convection *** implementation is simple,including on the block-structured adaptive *** efficiency of the S-L method is demonstrated by extensive numerical examples including passive convection of interfaces with corners/kinks/large deformation under given velocity fields,a geometrical flow with topological changes,simulations of bubble/droplet dynamics in incompressible twophase *** terms of accuracy it is comparable to the other existing methods.

关键词： semi-lagrangian method level-set method interface motion two-phase flow bubble/droplet dynamics block-structured adaptive mesh

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Multispectrum method and the Computation of Vapor Equation

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Advances in Atmospheric Sciences 1997年第4期14卷 132-137页

作者：季仲贞王斌 LASG Institute of Atmospheric Physics Chinese Academy of Sciences 100029

In order to improve the practicality of spectral method and the efficiency of computation, the multi-spectrum method is proposed on the basis of multi-grid method. Coarse spectra are used to compute the slow nonlinear part (including physical process), while fine spectra are used to compute the fast linear part. This method not only can reduce computation time, but also can obtain computational efficiency similar to that from only fine spectra. Thus, it is an economical numerical method. Both explicit complete-square-conservation scheme and multispectrum scheme are used to improve IAP L 9 T 42 spectral climate models, with and without physical forcings respectively, and the advantage of reducing computation time is obtained satisfactorily. In order to overcome the difficulty that vapor equation is very sensitive to the change of time step, the square-conservation semi-lagrangian scheme is used to solve vapor equation. Because the semi-lagrangian scheme has the property of square-conservation, computational instability can be avoided. When time step becomes longer with the semi-lagrangian Scheme, through numerical examples, the vapor transportation can be depicted objectively and the effect of precipitation simulation can be modified.

关键词： Spectral method Multispectrum semi-lagrangian method Computation of vapor

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A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses

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Plasma Science and Technology 2022年第2期24卷 117-126页

作者： Zhexu WANG Rei KAWASHIMA Kimiya KOMURASAKI Univ Tokyo Bunkyo Ku 7-3-1 Hongo Tokyo 1138656 Japan

A 1D1 V hybrid Vlasov-fluid model was developed for this study to elucidate discharge current oscillations of Hall thrusters(HTs).The Vlasov equation for ions velocity distribution function with ionization source term is solved using a constrained interpolation profile conservative semilagrangian *** fourth-order weighted essentially non-oscillatory(4 th WENO)limiter is applied to the first derivative value to minimize numerical oscillation in the discharge oscillation *** fourth-order accuracy is verified through a 1 D scalar test *** and high-resolution features of the Vlasov model are confirmed by simulating the test cases of the Vlasov–Poisson system and by comparing the results with a particle-in-cell(PIC)method.A1 D1 V HT simulation is performed through the hybrid Vlasov *** ionization oscillation is *** oscillation amplitude and plasma density are compared with those obtained from a hybrid PIC *** comparison indicates that the hybrid Vlasov-fluid model yields noiseless results and that the steady-state waveform is calculable in a short time period.

关键词： Hall thruster ionization oscillation Vlasov equation semi-lagrangian method

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Improvement of the semi-lagrangian Advection Scheme in the GRAPES Model:Theoretical Analysis and Idealized Tests

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Advances in Atmospheric Sciences 2014年第3期31卷 693-704页

作者： HUANG Bo CHEN Dehui LI Xingliang LI Chao Chinese Academy of Meteorological Sciences Numerical Weather Prediction Center China Meteorological Administration University of Chinese Academy of Sciences

ABSTRACT The Global/Regional Assimilation and PrEdiction System （GRAPES） is the newgeneration numerical weather predic- tion （NWP） system developed by the China Meteorological Administration. It is a fully compressible non-hydrostatical global/regional unified model that uses a traditional semi-lagrangian advection scheme with cubic lagrangian interpola tion （referred to as the SL_CL scheme）. The SL_CL scheme has been used in many operational NWP models, but there are still some deficiencies, such as the damping effects due to the interpolation and the relatively low accuracy. Based on Reich＇s semi-lagrangian advection scheme （referred to as the R2007 scheme）, the Re_R2007 scheme that uses the low- and high-order B-spline function for interpolation at the departure point, is developed in this paper. One- and two-dimensional idealized tests in the rectangular coordinate system with uniform grid cells were conducted to compare the Re..R2007 scheme and the SL_CL scheme. The numerical results showed that：（1） the damping effects were remarkably reduced with the Re_R2007 scheme; and （2） the normalized errors of the Re_R2007 scheme were about 7.5 and 3 times smaller than those of the SL_CL scheme in one- and two-dimensional tests, respectively, indicating the higher accuracy of the Re..R2007 scheme. Furthermore, two solid-body rotation tests were conducted in the latitude-longitude spherical coordinate system with non uniform grid cells, which also verified the Re_R2007 scheme＇s advantages. Finally, in comparison with other global advection schemes, the Re_R2007 scheme was competitive in terms of accuracy and flow independence. An encouraging possibility for the application of the Re_R2007 scheme to the GRAPES model is provided.

关键词： numerical models semi-lagrangian method advection scheme numerical accuracy spline interpolation

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A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampere Equations

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Communications in Computational Physics 2011年第9期10卷 1001-1026页

作者： Nicolas Crouseilles Thomas Respaud INRIA-Nancy-Grand Est CALVI ProjectStrasbourgFrance IRMA Universite de Strasbourg and INRIA-Nancy-Grand EstCALVI ProjectStrasbourgFrance

In this report,a charge preserving numerical resolution of the 1D VlasovAmp`ere equation is achieved,with a forward semi-lagrangian method introduced in[10].The Vlasov equation belongs to the kinetic way of simulating plasmas evolution,and is coupled with the Poisson’s equation,or equivalently under charge conservation,the Amp`ere’s one,which self-consistently rules the electric field *** order to ensure having proper physical solutions,it is necessary that the scheme preserves charge numerically.B-spline deposition will be used for the interpolation *** solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure.

关键词： semi-lagrangian method charge conservation Runge-Kutta Cauchy-Kovalevsky B-spline deposition

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