FEMLAB - KTH

More documents

Recommendations

Info

Cf = C ρwCw + ρ f and the concentration involved in chemical reaction is given by C Cw = KpCf = Kp ρwCw + ρ f 14 (4.23) (4.24)
Chapter 5 Model Implementation with FEMLAB 5.1 The Femlab Software FEMLAB is a software package for the simulation and visualisation of partial differential equations in one, two or three dimensions. The simulations are based on the finite element method, abbreviated as FEM, hence the name FEMLAB. It performs equation-based multiphysics modelling [13, p.153]. This means that we can formulate our equations so that they actually suit our problem. The physical domain is represented graphically in the software, and this is called the geometry, or computational domain. If various parts of the physical domain have different properties or phenomena, then the computational domain can be differentiated into subdomains which will have different parameters and, maybe, equations. The underlying mathematical structure of FEMLAB is a system of partial differential equations (PDE)s. There are many application modes in FEMLAB, suitable for various scientific problems. These are, so to speak, templates for defined equations which can be modified by changing the values of some predefined parameters, to suit the scientific problems we want to solve. The problem at hand does not fit well into the predefined application modes. Therefore the coefficient form of the PDE mode is used in this work. In this mode, one physics mode[10, p.8] can handle many variables. Since there are at least two variables in each part of the cell, this property is very useful for the present model. 5.2 The Geometry A 2D model is sufficient for our purpose. A sector of only one-sixteenth (22.5 o ) of the cell is used to minimise computational resources and time. Thickness of the nucleus was used as the scaling factor. All parts of the cell are scaled with this factor s. 15
Page 1 and 2: Mathematical Modelling and Numerica
Page 3 and 4: Abstract In order to shed more ligh
Page 5 and 6: Contents 1 Introduction 1 2 The Phy
Page 7 and 8: Chapter 1 Introduction The aim of t
Page 9 and 10: Chapter 2 The Physical Problem and
Page 11 and 12: Ci + water −→ Ui at rate kiCi (
Page 13 and 14: Chapter 3 Scaling and Reformulation
Page 15 and 16: Chapter 4 Simplification of problem
Page 17 and 18: and since ▽ 2 φ is constant over
Page 19: 4.3 Solving for concentration; Frac
Page 23 and 24: Figure 5.1. The computational Domai
Page 25 and 26: Physical subdomain Femlab Subdomain
Page 27 and 28: Figure 5.3. C in solution plotted a
Page 29 and 30: Figure 6.1. Concentration of A in t
Page 31: List of Abbreviations A . . . . . .

FEMLAB - KTH

Create successful ePaper yourself

Delete template?

Save as template?