This work proposes the nonlinear model for the flow of mixture of compressible liquids in a porous medium with consideration of finite deformations and thermal effects. Development of this model is based on the method of thermodynamically consistent systems of conservation laws. Numerical analysis of the model is based on the WENO-Runge-Kutta method of the high accuracy. The model is developed to solve the problems arising when studying the different-scale fluid dynamic processes. Evolution of the wave fields in inhomogeneous saturated porous media is considered.