© 2022 IMACSWe introduce an artificial compression (AC) method for simulations of the MHD system in Elsässer Variables. The proposed method decouples unknowns such as pressure, which acts as a Lagrange multiplier ensuring divergence constraints in each equation, from velocity and magnetic field vectors. By advancing for each unknown explicitly in time, the method approximates flow quantities at a lower cost when compared with its fully-implicit counterparts. We propose backward Euler and BDF2 based AC methods for MHD systems. This report presents stability and accuracy analyses of the proposed methods and numerically verifies the theoretical findings.