  Weyl semimetal, which does not require any symmetry except translation for
protection, is a robust gapless state of quantum matters in three dimensions.
When translation symmetry is preserved, the only way to destroy a Weyl
semimetal state is to bring two Weyl nodes of opposite chirality close to each
other to annihilate pairwise. An external magnetic field can destroy a pair of
Weyl nodes (which are separated by a momentum space distance $2k_0$) of
opposite chirality, when the magnetic length $l_B$ becomes close to or smaller
than the inverse separation $1/2k_0$. In this work, we investigate pairwise
annihilation of Weyl nodes induced by external magnetic field which ranges all
the way from small to a very large value in the Hofstadter regime $l_B \sim a$.
We show that this pairwise annihilation in a WSM featuring two Weyl nodes leads
to the emergence of either a normal insulator or a layered Chern insulator. In
the case of a Weyl semimetal with multiple Weyl nodes, the potential for
generating a variety of states through external magnetic fields emerges. Our
study introduces a straightforward and intuitive representation of the pairwise
annihilation process induced by magnetic fields, enabling accurate predictions
of the phases that may appear after pairwise annihilation of Weyl nodes.
