  We investigate the coupled dynamics of quantized vortices and normal fluid in
superfluid $^4$He at finite temperatures using a numerical approach based on
the vortex filament model (VFM) and lattice Boltzmann method (LBM). The LBM
allows us to simulate a fluid flow with only local operations, i .e., rather
than solving the Navier--Stokes (NS) equations directly; a fluid flow is
considered a convection of mesoscopic particles between sites on a lattice
grid. Although the two-fluid nature of He II makes its flow complex, the
particle-like treatment of the normal fluid in the LBM significantly reduces
the complexity. We confirm, by comparing to results obtained with direct NS
simulations, that the proposed numerical approach reproduces characteristic
flow structures. We also demonstrate that the proposed computational approach
is suitable for a thermal counterflow simulation with a solid boundary to
elucidate a thermal boundary layer near a heater in a closed channel.
