  Weyl semimetals, featuring massless linearly dispersing chiral fermions in
three dimensions, provide an excellent platform for studying the interplay of
electronic interactions and topology, and exploring new correlated states of
matter. Here, we examine the effect of a local repulsive interaction on an
inversion-symmetry breaking Weyl semimetal model, using cluster dynamical mean
field theory and variational cluster approximation methods. Our analysis
reveals a continuous transition from the gapless Weyl semimetal phase to a
gapped spin density wave ordered phase at a critical value of the interaction,
which is determined by the band structure parameters. Further, we introduce a
finite tilt in the linear dispersion and examine the corresponding behavior for
a type-II Weyl semimetal model, where the critical interaction strength is
found to be significantly diminished, indicating a greater susceptibility
towards interactions. The behavior of different physical quantities, such as
the double occupancy, the spectral function and the Berry curvature associated
with the Weyl nodes are obtained in both the semimetallic and the magnetically
ordered states. Finally, we provide an interaction-induced phase diagram for
the Weyl semimetal model, as a function of the tilt parameter.
