This paper presents a numerical implementation of boundary conditions in the finite difference staggered grid method for a Hyperbolic Thermodynamically Compatible (HTC) model of wavefields simulations in a three-phase model of a deformable porous medium saturated with a mixture of two fluids. A number of test problems on the propagation of high-frequency waves have been solved and it has been shown that the developed numerical method is applicable to non-stationary processes in domains of complex structure. The method can also be applied to obtain a steady-state solution of the equilibrium equations of a saturated porous medium by solving a nonstationary system.