Novel pressure-correction schemes based on scalar auxiliary variable method for the MHD equations

This work introduces a novel schemes that combines scalar auxiliary variable (SAV) and pressure-correction (PC) method to solve the magneto-hydrodynamic (MHD) equations. Prove that the first-order and the second-order PC-SAV scheme are unconditionally energy stable. Moreover, the results obtained by our numerical experiments can well verify the effectiveness of the schemes. Finally, the PC-SAV adaptive time-stepping method is given that improve efficiency.