A Finite Element Implementation for the Three Variable Biot Model and an Introduction to its Application to Sugar Cane Milling Processes

Abstract

This document presents a step-by-step derivation for the formulation of a Biot model for saturated porous media, this formulation is apt to be implemented both in two and three dimensions. Afterwards, the spatial and temporal discretization for the model is also presented, focusing on a symbolic representation around the Gauss points for a particular element in an implementation. Lastly, the results for a couple of test cases are shown, and of special interest, the test case that constitutes the first approximation towards an implementation of this model for the simulation of sugar cane milling processes.