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Gas-kinetic numerical schemes for one- and two-dimensional inner flows
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作者 李志辉 毕林 唐志共 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第7期889-904,共16页
Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics ... Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated aad analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed. 展开更多
关键词 Boltzmann model equation gas-kinetic numerical schemes discrete velocityordinate method shock-tube problems channel flows
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NUMERICAL SIMULATION OF SUPERSONIC AXISYMMETRIC FLOW OVER MISSILE AFTERBODY WITH JET EXHAUST USING POSITIVE SCHEMES 被引量:1
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作者 朱孙科 马大为 +1 位作者 陈二云 乐贵高 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2011年第3期255-261,共7页
Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the... Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise. 展开更多
关键词 computational fluid dynamics supersonic flow positive schemes numerical simulation
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The Sensitivity of Numerical Simulation of the East Asian Monsoon to Different Cumulus Parameterization Schemes 被引量:2
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作者 成安宁 陈文 黄荣辉 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 1998年第2期71-87,共17页
In this paper, a 5-level spectral AGCM is used to examine the sensitivity of simulated East Asian summer monsoon circulation and rainfall to cumulus parameterization schemes. From the simulated results of East Asian ... In this paper, a 5-level spectral AGCM is used to examine the sensitivity of simulated East Asian summer monsoon circulation and rainfall to cumulus parameterization schemes. From the simulated results of East Asian monsoon circulations and rainfalls during the summers of 1987 and 1995, it is shown that the Kuo′s convective parameterization scheme is more suitable for the numerical simulation of East Asian summer monsoon rainfall and circulation. This may be due to that the cumulus in the rainfall system is not strong in the East Asian monsoon region. 展开更多
关键词 Convective parameterization scheme East Asian monsoon numerical simulation
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NUMERICAL SCHEMES WITH HIGH ORDER OF ACCURACY FOR THE COMPUTATION OF SHOCK WAVES 被引量:1
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作者 袁湘江 周恒 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第5期489-500,共12页
High order accurate scheme is highly desirable for Slow computation with shocks. After analysis has been made for the reason of the generation of non-physical oscillations around the shock in numerical computations, a... High order accurate scheme is highly desirable for Slow computation with shocks. After analysis has been made for the reason of the generation of non-physical oscillations around the shock in numerical computations, a third-order, upwind biased, shock capturing scheme was proposed. Also, a new shock fitting method, called pseudo shock fitting method, was suggested, which in principle can be with any order of accuracy. Test cases for one dimensional flows show that the new method is very satisfactory. 展开更多
关键词 numerical method computation of shock waves upwind compact scheme
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Lagrangian model of zooplankton dispersion:numerical schemes comparisons and parameter sensitivity tests 被引量:1
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作者 丘仲锋 Andrea M.DOGLIOLI +1 位作者 何宜军 Francois CARLOTTI 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 2011年第2期438-445,共8页
This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion:numerical schemes and time steps.Firstly,we compared three numerical schemes using idealized circulations.Results show that... This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion:numerical schemes and time steps.Firstly,we compared three numerical schemes using idealized circulations.Results show that the precisions of the advanced Adams-Bashfold-Moulton(ABM) method and the Runge-Kutta(RK) method were in the same order and both were much higher than that of the Euler method.Furthermore,the advanced ABM method is more efficient than the RK method in computational memory requirements and time consumption.We therefore chose the advanced ABM method as the Lagrangian particle-tracking algorithm.Secondly,we performed a sensitivity test for time steps,using outputs of the hydrodynamic model,Symphonie.Results show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity fields.The method introduced by Oliveira et al.in 2002 is suitable for choosing time steps of Lagrangian particle-tracking models,at least when only considering advection. 展开更多
关键词 LAGRANGIAN numerical scheme time steps ZOOPLANKTON
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Sensitivity of Numerical Simulations of the East Asian Summer Monsoon Rainfall and Circulation to Different Cumulus Parameterization Schemes
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作者 黄荣辉 武炳义 +1 位作者 洪胜吉 吴载镐 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2001年第1期23-41,共19页
A 5-level spectral AGCM (ImPKU-SLAGCM) is used to examine the sensitivity of the simulated results of the summer monsoon rainfall and circulation in East Asia to different cumulus parameterization schemes in the clima... A 5-level spectral AGCM (ImPKU-SLAGCM) is used to examine the sensitivity of the simulated results of the summer monsoon rainfall and circulation in East Asia to different cumulus parameterization schemes in the climatological-mean case and in the cases of weak and strong Asian summer monsoons, respectively. The results simulated with the Arakawa-Schubert's(hereafter A-S's), Kuo's and Manabe's cumulus parameterization schemes show that these simulated distributions of the summer monsoon rainfall and circulation in East Asia depend strongly on the cumulus parameterization schemes either in the climatological-mean case or in the cases of weak and strong Asian summer monsoons. From the simulated results, it might be shown that the Kuo scheme appears to be more suitable for the simulation of the summer monsoon rainfall and circulation in East Asia than the A-S scheme or the Manabe scheme, although the A-S scheme is somewhat better in the simulations of the tropical rainfall. This might be due to that the Kuo's cumulus parameterization scheme is able to reflect well the characteristics of rainfall cloud system in the East Asian summer monsoon region, where the rainfall system used to be a mixing of cumulus and stratus. 展开更多
关键词 numerical simulation East Asian summer monsoon cumulus parameterization scheme
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The Simulating of Power Electronics Systems with the Use of Explicit Numerical Schemes
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作者 Yuri Tanovitski Gennady Kobzev 《Applied Mathematics》 2013年第1期223-227,共5页
Automated simulating of power electronics systems is currently performed by means of nodal analysis method combined with implicit numerical integration schemes. Such method allows to find transient solutions, even whe... Automated simulating of power electronics systems is currently performed by means of nodal analysis method combined with implicit numerical integration schemes. Such method allows to find transient solutions, even when the integrated system is stiff, however, it leads to some difficulties when simulating big systems and sometimes to the deterioration of computations quality, that is reflected in decrease in accuracy, oscillations of solutions, which are not present in the initial model. This paper analyzes the shortcomings of this approach, and proposes to apply explicit numerical schemes with stability control on the integration step and with reduction of some of state variables. A brief description of the method of finding transient solutions and an example of the analysis are also given in the present paper. 展开更多
关键词 TRANSIENT Analysis IMPLICIT EXPLICIT numerical schemes Power ELECTRONICS
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A Survey of the Implementation of Numerical Schemes for Linear Advection Equation
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作者 Pedro Pablo Cárdenas Alzate 《Advances in Pure Mathematics》 2014年第8期467-479,共13页
The interpolation method in a semi-Lagrangian scheme is decisive to its performance. Given the number of grid points one is considering to use for the interpolation, it does not necessarily follow that maximum formal ... The interpolation method in a semi-Lagrangian scheme is decisive to its performance. Given the number of grid points one is considering to use for the interpolation, it does not necessarily follow that maximum formal accuracy should give the best results. For the advection equation, the driving force of this method is the method of the characteristics, which accounts for the flow of information in the model equation. This leads naturally to an interpolation problem since the foot point is not in general located on a grid point. We use another interpolation scheme that will allow achieving the high order for the box initial condition. 展开更多
关键词 numerical schemes Advection EQUATION SEMI-LAGRANGIAN Approach
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Nonstandard Numerical Schemes for a Linear Stochastic Oscillator with Additive Noise
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作者 姚金然 甘四清 《Journal of Donghua University(English Edition)》 EI CAS 2017年第5期694-701,共8页
In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique... In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique.These proposed schemes reproduce long time features of the oscillator solution exactly.Their abilities in preserving the symplecticity,the linear growth property of the second moment and the oscillation property of the solution of the stochastic oscillator system on long time interval are studied.It can be shown that the component { x_n}_(n≥1) of the INSOPT schemes switch signs infinitely many times as n →∞,almost surely.Further,the mean-square convergence order of 1 is obtained for these INSOPT schemes.Finally,numerical experiments illustrate intuitively the results obtained in this paper. 展开更多
关键词 linear stochastic oscillator nonstandard numerical scheme long time behavior
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Numerical Simulation of Modified Kortweg-de Vries Equation by Linearized Implicit Schemes
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作者 M. S. Ismail Fakhirah Alotaibi 《Applied Mathematics》 2020年第11期1139-1161,共23页
In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two ... In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two nonlinear schemes and two linearized schemes are presented. All resulting schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities are used to highlight the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be also conducted. The numerical results show that the interaction behavior is elastic and the conserved quantities are conserved exactly, and this is a good indication of the reliability of the schemes which we derived. A comparison with some existing is presented as well. 展开更多
关键词 MKdV Equation Pade Approximation Nonlinear numerical schemes Linearly Implicit schemes Fixed Point Method Interaction of Solitons
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Numerical Simulation of Bed Load and Suspended Load Sediment Transport Using Well-Balanced Numerical Schemes
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作者 J.C.González-Aguirre J.A.González-Vázquez +2 位作者 J.Alavez-Ramírez R.Silva M.E.Vázquez-Cendón 《Communications on Applied Mathematics and Computation》 2023年第2期885-922,共38页
Sediment transport can be modelled using hydrodynamic models based on shallow water equations coupled with the sediment concentration conservation equation and the bed con-servation equation.The complete system of equ... Sediment transport can be modelled using hydrodynamic models based on shallow water equations coupled with the sediment concentration conservation equation and the bed con-servation equation.The complete system of equations is made up of the energy balance law and the Exner equations.The numerical solution for this complete system is done in a seg-regated manner.First,the hyperbolic part of the system of balance laws is solved using a finite volume scheme.Three ways to compute the numerical flux have been considered,the Q-scheme of van Leer,the HLLCS approximate Riemann solver,and the last one takes into account the presence of non-conservative products in the model.The discretisation of the source terms is carried out according to the numerical flux chosen.In the second stage,the bed conservation equation is solved by using the approximation computed for the system of balance laws.The numerical schemes have been validated making comparisons between the obtained numerical results and the experimental data for some physical experiments.The numerical results show a good agreement with the experimental data. 展开更多
关键词 Sediment transport Suspended load Bed load Finite volume method numerical simulation Well-balanced schemes
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A numerical study for some efficient time-integration schemes using barotropic equations
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作者 Han Wei and Zhang Yuling Department of Geophysics, Peking University, Beijing, China 《Acta Oceanologica Sinica》 SCIE CAS CSCD 1989年第1期77-89,共13页
Three kinds of methods, i. e., explicit, semi-implicit, and semi-implicit and semi-Lagrangian method, are tested in the time-integration of shallow-water equations on rotating sphere. Helpful results are available fro... Three kinds of methods, i. e., explicit, semi-implicit, and semi-implicit and semi-Lagrangian method, are tested in the time-integration of shallow-water equations on rotating sphere. Helpful results are available from experiments, especially about the accuracy and efficiency of different semi-implicit and semi-Lagrangian schemes. 展开更多
关键词 time A numerical study for some efficient time-integration schemes using barotropic equations
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SEVERAL NEW TYPES OF FINITE-DIFFERENCE SCHEMES FOR SHALLOW-WATER EQUATION WITH INITIAL-BOUNDARY VALUE AND THEIR NUMERICAL EXPERIMENT
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作者 吕秋强 周钢 刘应中 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第3期271-281,共11页
This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative... This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. A t last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave. 展开更多
关键词 In SEVERAL NEW TYPES OF FINITE-DIFFERENCE schemes FOR SHALLOW-WATER EQUATION WITH INITIAL-BOUNDARY VALUE AND THEIR numerical EXPERIMENT
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A unified gas-kinetic scheme for multiscale and multicomponent flow transport 被引量:4
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作者 Tianbai XIAO Kun XU Qingdong CAI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2019年第3期355-372,共18页
Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of diffe... Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to construct an accurate and efficient numerical algorithm to faithfully represent multiscale flow physics across different regimes. In this paper, a unified gas-kinetic scheme(UGKS) is developed to study non-equilibrium multicomponent gaseous flows. Based on the Boltzmann kinetic equation, an analytical space-time evolving solution is used to construct the discretized equations of gas dynamics directly according to cell size and scales of time steps, i.e., the so-called direct modeling method. With the variation in the ratio of the numerical time step to the local particle collision time(or the cell size to the local particle mean free path), the UGKS automatically recovers all scale-dependent flows over the given domain and provides a continuous spectrum of the gas dynamics. The performance of the proposed unified scheme is fully validated through numerical experiments.The UGKS can be a valuable tool to study multiscale and multicomponent flow physics. 展开更多
关键词 UNIFIED gas-kinetic scheme(UGKS) multiscale modeling MULTICOMPONENT flow
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The study of sound wave propagation in rarefied gases using unified gas-kinetic scheme 被引量:5
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作者 Rui-Jie Wang Kun Xu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第4期1022-1029,共8页
Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme (UGKS). The numerical calculations are carfled out for a wide range of wave oscillating frequencies. ... Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme (UGKS). The numerical calculations are carfled out for a wide range of wave oscillating frequencies. The corresponding rarefaction parameter is defined as the ratio of sound wave frequency to the intermolecular particle collision frequency. The simulation covers the flow regime from the continuum to free molecule one. The treatment of the os- cillating wall boundary condition and the methods for eval- uating the absorption coefficient and sound wave speed are presented in detail. The simulation results from the UGKS are compared to the Navier-Stokes solutions, the direct sim- ulation Monte Carlo (DSMC) simulation, and experimental measurements. Good agreement with the experimental data has been obtained in the whole flow regimes for the corresponding Knudsen number from 0.08 to 32. The cur- rent study clearly demonstrates the capability of the UGKS method in capturing the sound wave propagation and its usefulness for the rarefied flow study. 展开更多
关键词 Unified gas-kinetic scheme Sound wave propagation- Non-equilibrium flows
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An Application of Finite Volume WENO Schemeto Numerical Modeling of Tidal Current 被引量:2
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作者 杨中华 槐文信 曾小辉 《China Ocean Engineering》 SCIE EI 2006年第4期545-556,共12页
A depth-averaged 2-D numerical model for unsteady tidal flow in estuaries is established by use of the finite volume WENO scheme which maintains both uniform high order accuracy and an essentially non-oscillatory shoc... A depth-averaged 2-D numerical model for unsteady tidal flow in estuaries is established by use of the finite volume WENO scheme which maintains both uniform high order accuracy and an essentially non-oscillatory shock transition on unstructured triangular grid. The third order TVD Range-Kutta method is used for time discretization. The model has been firstly tested against four cases: 1) tidal forcing, 2) seiche oscillation, 3) wind setup in a closed bay, and 4) onedimensional dam-break water flow. The results obtained in the present study compare well with those obtained from the corresponding analytic solutions idealized for the above four cases. The model is then applied to the simulation of tidal circulation in the Yangpu Bay, and detailed model calibration and verification have been conducted with measured tidal current in the spring tide, middle tide, and neap tide. The overall performance of the model is in qualitative agreement with the data observed in 2005, and it can be used to calculate the flow in estuaries and coastal waters. 展开更多
关键词 tidal current numerical modeling WENO scheme unstructured triangular grid
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A Hybrid SIR-Fuzzy Model for Epidemic Dynamics:A Numerical Study
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作者 Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第6期3417-3434,共18页
This study focuses on the urgent requirement for improved accuracy in diseasemodeling by introducing a newcomputational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious... This study focuses on the urgent requirement for improved accuracy in diseasemodeling by introducing a newcomputational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious-Recovered(SIR)modelwith fuzzy logic,ourmethod effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters.The main aim of this research is to provide a model for disease transmission using fuzzy theory,which can successfully address uncertainty in mathematical modeling.Our main emphasis is on the imprecise transmission rate parameter,utilizing a three-part description of its membership level.This enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical models.We investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis,providing insight into the complex correlation betweenmodel parameters and epidemic results.In order to facilitate a quantitative analysis of the fuzzy model,we propose the implementation of a resilient numerical scheme.The convergence study of the scheme demonstrates its trustworthiness,providing a conditionally positive solution,which represents a significant improvement compared to current forward Euler schemes.The numerical findings demonstrate themodel’s effectiveness in accurately representing the dynamics of disease transmission.Significantly,when the mortality coefficient rises,both the susceptible and infected populations decrease,highlighting the model’s sensitivity to important epidemiological factors.Moreover,there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected,as well as an increase in the number of susceptible individuals.This correlation offers a significant understanding of how many elements affect the consequences of an epidemic.Our objective is to enhance decision-making in public health by providing a thorough quantitative analysis of the Hybrid SIR-Fuzzy Model.Our approach not only tackles the existing constraints in disease modeling,but also paves the way for additional investigation,providing a vital instrument for researchers and policymakers alike. 展开更多
关键词 Fuzzy-based model sensitivity equilibriumpoints proposed numerical scheme convergence and stability analysis
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Optimal Evacuation Scheme Based on Dam-Break Flood Numerical Simulation 被引量:2
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作者 王晓玲 孙蕊蕊 +1 位作者 周正印 黄凌 《Transactions of Tianjin University》 EI CAS 2011年第6期424-430,共7页
The optimal evacuation scheme is studied based on the dam-break flood numerical simulation. A three- dimensional dam-break mathematical model combined with the volume of fluid (VOF) method is adopted. According to t... The optimal evacuation scheme is studied based on the dam-break flood numerical simulation. A three- dimensional dam-break mathematical model combined with the volume of fluid (VOF) method is adopted. According to the hydraulic information obtained from numerical simulation and selecting principles of evacuation emergency scheme, evacuation route analysis model is proposed, which consists of the road right model and random degree model. The road right model is used to calculate the consumption time in roads, and the random degree model is used to judge whether the roads are blocked. Then the shortest evacuation route is obtained based on Dijstra algorithm. Gongming Reservoir located in Shenzhen is taken as a case to study. The results show that industrial area I is flooded at 2 500 s, and after 5 500 s, most of industrial area II is submerged. The Hushan, Loucun Forest and Chaishan are not flooded around industrial area I and II. Based on the above analysis, the optimal evacuation scheme is determined. 展开更多
关键词 three-dimensional dam-break numerical model volume of fluid method evacuation route analysis model evacuation scheme
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A New Second Order Numerical Scheme for Solving Forward Backward Stochastic Differential Equations with Jumps 被引量:1
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作者 Hongqiang Zhou Yang Li Zhe Wang 《Applied Mathematics》 2016年第12期1408-1414,共8页
In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator  linearly depending on . And we theoretically prove that the conv... In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator  linearly depending on . And we theoretically prove that the convergence rates of them are of second order for solving  and of first order for solving  and  in  norm. 展开更多
关键词 numerical scheme Error Estimates Backward Stochastic Differential Equations
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A CLASS OF TWO-STEP TVD MACCORMACK TYPE NUMERICAL SCHEME FOR MHD EQUATIONS 被引量:1
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作者 FENG Xueshang WEI Fengsi ZHONG Dingkun(Center for Space Science and Applied Research, The Chinese Academy of Sciences, Beijing 100080) 《空间科学学报》 CAS CSCD 北大核心 2003年第6期401-412,共12页
In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stabili... In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities. 展开更多
关键词 磁液体力学方程 两步TVD-MacCormack图解法 收敛性 稳定性 数值模拟
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