When the relaxation time (or Knudsen number) is sufficiently small, the lattice Boltzmann equation
(LBE) recovers the governing Navier-Stokes equations in macroscopic scales. However, as the shear
viscosity directly relates to the relaxation time, increasing the system viscosity requires increasing
the relaxation time value. Therefore, the second-order error terms of the relaxation time may be-
come significant at high viscounties, especially in multiphase systems with a high-density contrast
between the two phases. To alleviate this issue, we added a source term with a free parameter to the
standard LBE, such that the fluid viscosity correlates with the free parameter and relaxation time.
In this way, the leading-order errors of viscosity can be suppressed by increasing the introduced free
parameter, which decreases the relaxation time value at the same viscosity. The numerical results
for a static droplet show that the proposed model can reduce the spurious velocities around the
interface by almost an order of magnitude.