Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations

@article{Li2021StabilityAE,
  title={Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations},
  author={Xiaoli Li and Weilong Wang and Jie Shen},
  journal={SIAM J. Numer. Anal.},
  year={2021},
  volume={60},
  pages={1026-1054}
}
Abstract. We construct and analyze firstand second-order implicit-explicit (IMEX) schemes based on the scalar auxiliary variable (SAV) approach for the magneto-hydrodynamic equations. These schemes are linear, only require solving a sequence of linear differential equations with constant coefficients at each time step, and are unconditionally energy stable. We derive rigorous error estimates for the velocity, pressure and magnetic field of the first-order scheme in the two dimensional case… 

Unconditionally energy-stable schemes based on the SAV approach for the inductionless MHD equations

In this paper, we consider numerical approximations for solving the inductionless magnetohydrodynamic (MHD) equations. By utilizing the scalar auxiliary variable (SAV) approach for dealing with the

Unconditional stability and error analysis of an Euler IMEX-SAV scheme for the micropolar Navier-Stokes equations

In this paper, we consider numerical approximations for solving the micropolar Navier-Stokes (MNS) equations, that couples the Navier-Stokes equations and the angular momentum equation together. By

Second order, unconditionally stable, linear ensemble algorithms for the magnetohydrodynamics equations

We propose two unconditionally stable, linear ensemble algorithms with pre-computable shared coefficient matrices across different realizations for the magnetohydrodynamics equations. The viscous terms

References

SHOWING 1-10 OF 32 REFERENCES

Efficient splitting schemes for magneto-hydrodynamic equations

It is shown that these semi-discretized schemes based on the standard and rotational pressure-correction schemes for the Navier-Stokes equations are unconditionally energy stable, present an effective algorithm for their fully discrete versions and carry out demonstrative numerical experiments.

Second order unconditionally convergent and energy stable linearized scheme for MHD equations

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.

New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis

New first- and second-order pressure correction schemes using the scalar auxiliary variable (SAV) approach for the Navier-Stokes equations are constructed, which are linear, decoupled and unconditionally energy stable.

Stable discretization of magnetohydrodynamics in bounded domains

We study a semi-implicit time-difference scheme for magnetohydrodynamics of a viscous and resistive incompressible fluid in a bounded smooth domain with a perfectly conducting boundary. In the

On the Long-Time H2-Stability of the Implicit Euler Scheme for the 2D Magnetohydrodynamics Equations

  • F. Tone
  • Mathematics, Physics
    J. Sci. Comput.
  • 2009
This article discretizes the two-dimensional magnetohydrodynamics equations in time using the implicit Euler scheme and with the aid of the classical and uniform discrete Gronwall lemma, it is proved that the scheme is H2-uniformly stable in time.

Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

Unconditional convergence of the Euler semi-implicit scheme for the 3D incompressible MHD equations

Purpose – The purpose of this paper is to consider the numerical implementation of the Euler semi-implicit scheme for three-dimensional non-stationary magnetohydrodynamics (MHD) equations. The Euler

Numerical analysis of two partitioned methods for uncoupling evolutionary MHD flows

Two partitioned methods are introduced to solve evolutionary MHD equations in cases where NSE and Maxwell codes separately are needed, each possibly optimized for the subproblem's respective physics.

The scalar auxiliary variable (SAV) approach for gradient flows

On error estimates of projection methods for Navier-Stokes equations: first-order schemes

In this paper projection methods (or fractional step methods) are studied in the semi-discretized form for the Navier–Stokes equations in a two- or three-dimensional bounded domain. Error estimates