Résumé : Ideal magnetohydrodynamics (MHD) simulations are known to have problems in satisfying the solenoidal constraint (i.e. the divergence of magnetic field should be equal to zero, $

ablacdotvec{B} = 0$). The simulations become unstable unless specific measures have been taken.

In this thesis, a solenoidal constraint satisfying technique that allows discrete satisfaction of the solenoidal constraint up to the machine accuracy is presented and validated with a variety of test cases. Due to its inspiration from Chorin's artificial compressibility method developed for incompressible CFD applications, the technique was named as \