Journal Article10.1007/S10444-016-9508-6
Numerical analysis of a second order algorithm for simplified magnetohydrodynamic flows
Yao Rong,Yanren Hou,Yuhong Zhang +2 more
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TL;DR: A complete theoretical analysis is presented to prove that this algorithm is unconditionally stable, consistent and second order accuracy.
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Abstract: In this paper, we construct a second order algorithm based on the spectral deferred correction method for the time-dependent magnetohydrodynamics flows at a low magnetic Reynolds number. We present a complete theoretical analysis to prove that this algorithm is unconditionally stable, consistent and second order accuracy. Finally, two numerical examples are given to illustrate the convergence and effectiveness of our algorithm.
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Citations
Second order unconditionally convergent and energy stable linearized scheme for MHD equations
TL;DR: An efficient numerical scheme based on a second order backward difference formula for time derivative terms, extrapolated treatments in linearization for nonlinear terms and the mixed finite element method is used for spatial discretization for magnetohydrodynamics equations.
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Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem
TL;DR: In this paper , a fully discrete mixed finite element method was proposed for the continuous and semi-implicit Euler-seimimplicit schemes for the magnetohydrodynamics problem.
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An unconditionally stable artificial compression method for the time‐dependent groundwater‐surface water flows
TL;DR: In this paper , the authors proposed a second order, unconditionally stable artificial compression method for the fully evolutionary Stokes/Darcy and Navier-Stokes-Darcy equations that model the coupling surface and groundwater flows, and verified the stability and second-order convergence of the algorithm from theoretical analysis and numerical experiments.
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Numerical analysis of a 4th-order time parallel algorithm for the time-dependent Navier-Stokes equations
Wenjia Liu,Yanren Hou,Dandan Xue +2 more
TL;DR: In conclusion, within almost same time to BE, the (reduced) RIDC4 scheme could achieve 4th order accuracy in time direction, provided four cores are available.
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A second-order decoupled algorithm with different subdomain time steps for the non-stationary Stokes/Darcy model
Dandan Xue,Yanren Hou +1 more
TL;DR: A second-order decoupled algorithm with different subdomain time steps for the non-stationary Stokes/Darcy model based on the second- order spectral deferred correction method in time and the finite element method in space is proposed and analyzed.
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References
Existence of Electromagnetic-Hydrodynamic Waves
TL;DR: In this article, a conducting liquid is placed in a constant magnetic field and every motion of the liquid gives rise to an E. H. M. F. which produces electric currents.
1.4K
•Journal Article
On the Existence of Electromagnetic-Hydrodynamic Waves
TL;DR: In this paper, a conducting liquid is placed in a constant magnetic field and every motion of the liquid gives rise to an E.H.M.F. which produces electric currents.
990
Spectral Deferred Correction Methods for Ordinary Differential Equations
TL;DR: In this article, a new class of methods for the Cauchy problem for ordinary differential equations (ODEs) was introduced, where the original ODE was converted into the corresponding Picard equation and applied a deferred correction procedure in the integral formulation, driven by either the explicit or the implicit Euler marching scheme.
503
•Book
Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
Jean-Frédéric Gerbeau,Claude Le Bris,Tony Lelièvre +2 more
- 31 Aug 2006
TL;DR: In this article, the magnetohydrodynamics equations of one-fluid problems have been analyzed and approximations of these problems are given for one industrial application using MHD models.
386
On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics
TL;DR: In this paper, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed under certain conditions on the data, and an optimal estimate for the error of the approximate solution is given.