  The development of smooth particle magnetohydrodynamic (SPMHD) has
significantly improved the simulation of complex astrophysical processes.
However, the preservation the solenoidality of the magnetic field is still a
severe problem for the MHD. A formulation of the induction equation with a
vector potential would solve the problem. Unfortunately all previous attempts
suffered from instabilities. In the present work, we evolve the vector
potential in the Coulomb gauge and smooth the derived magnetic field for usage
in the momentum equation. With this implementation we could reproduce classical
test cases in a stable way. A simple test case demonstrates the possible
failure of widely used direct integration of the magnetic field, even with the
usage of a divergence cleaning method.
