Saturated particulate networks exhibiting compressive material behavior are formed during mechanical solid-liquid separations. Due to costly experiments in terms of money and time, numerical models and simulation approaches are used to support the design of separation devices. In this work a computationally-efficient method is proposed to simulate the equilibrium and transient consolidation of particulate networks in one dimension. It is based on the Eulerian approach for approximation of the volume fraction of the dispersed phase without solving any additional partial differential equations and is implemented in the open source platform OpenFOAM. Under certain restrictions, the approach allows coupling with transient and spatially resolved three-dimensional computational fluid dynamics simulations. Firstly, the general method is discussed, followed by validation with experiments in a compression-permeation cell, which also demonstrates the model's capability of handling elastic and plastic compression behaviour. Lastly, the suitability for coupling with CFD simulations is demonstrated with three-dimensional simulations of the separation process in a solid-bowl centrifuge.