  We use the wide-used \textsf{Einstein Toolkit} to solve the Einstein
constraints and then simulate the expansion of primordial black hole lattices
(PBHLs) with different value of $f_{\mathrm{PBH}}$ and $m_{\mathrm{PBH}}$. We
find that $f_{\mathrm{PBH}}$ plays an important role during the evolution of
PBHLs. Since the motion of primordial black holes (PBHs) caused by the
expansion of PBHLs occurs at speeds close to that of light, we expect the
emission of gravitational waves (GWs) during the expansion of PBHLs. We use
both analytical estimates and numerical simulations to cross check the
production of GWs in expanding PBHLs.
