are reasons to consider the mathematical foundation of the finite element approximation more accurate, for instance, because the quality of the approximation between grid points in FEM is often higher than in the corresponding FDM approach. The starting point for the finite element method is a mesh, a partition of the geometry into small units of a simple shape, mesh elements. Once we have a mesh, we can introduce approximations to the dependent variables. The idea is to approximate our variables with functions that can be described with a finite number of parameters or degrees of freedom (DOF). Inserting this approximation into the weak form of the equation generates a system of equations for the degrees of freedom [36]. The commercial package that we decided to use for our model using the FEM is COMSOL Multiphysics. This multiphysics simulation software has a number of predefined physics interfaces for advanced fluid flow and heat transfer phenomena. Material properties, source terms and boundary conditions can all be arbitrary functions of the dependent variables. The material parameters and boundary conditions are specified using features in a number of physics interfaces. Each physics interface forms one or several PDEs and boundary conditions from these settings. Then software collects all the equations and boundary conditions formulated by the physics interfaces into one large system of PDEs and boundary conditions. Governing equations Four physical processes are simulated in order to study the energy storage process: fluid flow, heat transfer by conduction and convection, and phase change heat transfer [37].
are reasons to consider the mathematical foundation of the finite element approximation more accurate, for instance, because the quality of the approximation between grid points in FEM is often higher than in the corresponding FDM approach. The starting point for the finite element method is a mesh, a partition of the geometry into small units of a simple shape, mesh elements. Once we have a mesh, we can introduce approximations to the dependent variables. The idea is to approximate our variables with functions that can be described with a finite number of parameters or degrees of freedom (DOF). Inserting this approximation into the weak form of the equation generates a system of equations for the degrees of freedom [36]. The commercial package that we decided to use for our model using the FEM is COMSOL Multiphysics. This multiphysics simulation software has a number of predefined physics interfaces for advanced fluid flow and heat transfer phenomena. Material properties, source terms and boundary conditions can all be arbitrary functions of the dependent variables. The material parameters and boundary conditions are specified using features in a number of physics interfaces. Each physics interface forms one or several PDEs and boundary conditions from these settings. Then software collects all the equations and boundary conditions formulated by the physics interfaces into one large system of PDEs and boundary conditions. Governing equations Four physical processes are simulated in order to study the energy storage process: fluid flow, heat transfer by conduction and convection, and phase change heat transfer [37].
Thesis_Draft_Irene_R-pa.docx