Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations
Xiaoli Li, Weilong Wang, Jie Shen
Abstract
We construct and analyze first- and second-order implicit-explicit schemes based on the scalar auxiliary variable 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 without any condition on the time step. Numerical examples are presented to validate the proposed schemes.
Topics & Concepts
MathematicsScalar (mathematics)Applied mathematicsConstant (computer programming)Stability (learning theory)Constant coefficientsPartial differential equationSequence (biology)Variable (mathematics)MagnetoMathematical analysisLinear equationGeometryComputer sciencePhysicsGeneticsQuantum mechanicsBiologyPower (physics)Programming languageMachine learningAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsNavier-Stokes equation solutions