Fundamentals of Numerical Methods & Simulation

CHEN40451 Fundamentals of Numerical Methods & Simulation 15 Semester 1 Undergraduate Level 4 Vahid Joekar-Niasar Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 Numerical modelling and simulations are essential to any engineering application. The numerical simulations are used to design, predict and assess a physical phenomenon or an engineering system. In subsurface energy engineering, there are varieties of applications including the carbon sequestration, heat extraction, groundwater flow and remediation, multiphase flow in porous media. To design projects for any of these applications, it is important to characterise, assess the system and perform numerical modelling to make sure the engineering designs will serve the objectives of the project. This unit provides the principal knowledge and fundamentals of a physical process can be simulated. Principles of numerical modelling and simulations will be covered in this unit. Following topics will be covered in this unit:<ul><li>Introduction to Flow Charts, how to design the pseudo-codes,</li><li>Introduction to syntax, commands and programming either in MALTAB (self-study),</li><li>Solving a non-linear equation using secant, bisection, Newton-Raphson Methods, with an example</li><li>Solving linear system of equations using Gauss elimination, LU decomposition, Gauss-seidel methods,</li><li>Application of Taylor series to discretise differential equations,</li><li>Introduction to the partial differential equations (PDEs) commonly used for subsurface energy and chemical engineering including hyperbolic, elliptic and parabolic equations.</li><li>Introduction to a computational problem; numerical domain, boundary and initial conditions,</li><li>Finite difference methods to solve elliptic and parabolic partial differential equations for mass, solute and energy conservations.</li><li>Convergence and numerical stability, </li><li>Introduction to finite difference and finite volume schemes,</li><li>Project on numerical simulation and programming related to the following problems</li><li>(1) heat transfer applicable to geothermal energy, heat exchangers, etc</li><li>(2) solute transport applicable to reaction engineering, geothermal energy, groundwater pollution</li><li>(3) mass transport in porous materials applicable to fluidised bed reactors, reservoir engineering, groundwater flow.</li></ul> Numerical modelling and simulations are essential to any engineering application. The numerical simulations are used to design, predict and assess a physical phenomenon or an engineering system. In subsurface energy engineering, there are varieties of applications including the carbon sequestration, heat extraction, groundwater flow and remediation, multiphase flow in porous media. To design projects for any of these applications, it is important to characterise, assess the system and perform numerical modelling to make sure the engineering designs will serve the objectives of the project. This unit provides the principal knowledge and fundamentals of a physical process can be simulated. Principles of numerical modelling and simulations will be covered in this unit. Following topics will be covered in this unit:<ul><li>Introduction to Flow Charts, how to design the pseudo-codes,</li><li>Introduction to syntax, commands and programming either in MALTAB (self-study),</li><li>Solving a non-linear equation using secant, bisection, Newton-Raphson Methods, with an example</li><li>Solving linear system of equations using Gauss elimination, LU decomposition, Gauss-seidel methods,</li><li>Application of Taylor series to discretise differential equations,</li><li>Introduction to the partial differential equations (PDEs) commonly used for subsurface energy and chemical engineering including hyperbolic, elliptic and parabolic equations.</li><li>Introduction to a computational problem; numerical domain, boundary and initial conditions,</li><li>Finite difference methods to solve elliptic and parabolic partial differential equations for mass, solute and energy conservations.</li><li>Convergence and numerical stability, </li><li>Introduction to finite difference and finite volume schemes,</li><li>Project on numerical simulation and programming related to the following problems</li><li>(1) heat transfer applicable to geothermal energy, heat exchangers, etc</li><li>(2) solute transport applicable to reaction engineering, geothermal energy, groundwater pollution</li><li>(3) mass transport in porous materials applicable to fluidised bed reactors, reservoir engineering, groundwater flow.</li></ul> This course aims to introduce the principles of numerical modelling and simulations, how an engineering problem can be translated into a mathematical equation, how to discretise the equation and how to numerically solve them. Programming of the numerical models will be the essential part of this module.  On the successful completion of the course, students will be able to:ILO 1: Develop flowcharts to deconvolute a given complex engineering problem to different steps of required for numerical modelling.ILO 2: Convert a pseudo-code to a computer program in MATLABILO 3: Develop the mathematical framework for an engineering problem with correct boundary and initial conditions, and governing equationsILO 4: Characterise the types of the partial differential equations for subsurface energy engineering with the associated numerical approachILO 5: Write the discretised form of a partial differential equation (related to geothermal subsurface energy or natural porous materials of energy devices such as fuel cells and batteries), and describe the expected numerical errors and accuracy in their discretised equations using the finite difference methodILO 6: Solve numerically the elliptic, parabolic and hyperbolic partial differential equations applicable to flow and transport in porous media (e.g., natural or engineered energy systems) using the finite difference methodILO 7: Solve an energy or engineering industrial problem by simplifying it, defining the boundary and initial conditions, employing correct governing equations and simulating it numerically. ILO 8: Complete group work activities and learn how to address the industrial problem within the industrial constraints (e.g. short notice, lack of data, etc) There will be delivered by a combination of lectures and computational laboratory delivered by blended online/in-class teaching. The theoretical parts will be covered in the lectures and practical knowledge will be developed in the computer cluster. 0 Other 100% <figure class="table"><table><tbody><tr><td>Assessment type</td><td> % Weighting within unit</td><td>Length</td><td>ILO tested</td></tr><tr><td>Formative Tutorial assignments</td><td>-</td><td>Take home</td><td>ILOs 1-6</td></tr><tr><td>Assignment 1 (test)</td><td>20%</td><td>In computer cluster</td><td>ILOs 1-6</td></tr><tr><td>Assignment 2 (continuous)</td><td>30%</td><td>In computer cluster </td><td>ILOs 1-8</td></tr><tr><td>Summative- Final exam</td><td>50%</td><td>1.5 hours </td><td>ILOs 1-6</td></tr></tbody></table></figure> MEng (Hons) Chem Eng MEng Chemical Engineering Fourth Year Optional MEng (Hons) Chem Eng w I E MEng (Hons) Chem Eng w I E Fourth Year Optional MEng (Hons) Chem Eng w SIE MEng Chem Eng w SIE Fourth Year Optional Core Reading ISE Numerical Methods for Engineers, 8th Edition, Steven C. Chapra, Raymond P. Canale, 2021Essential Reading Computational Methods for Multiphase Flows in Porous Media, Zhangxin Chen, Guanren Huan, Yuanle Ma, 2006.Recommended Reading MATLAB: A Practical Introduction to Programming and Problem Solving, Attaway, Boston UniversityFurther Reading Geological Storage of CO2 Modeling Approaches for Large-Scale Simulation, Jan Martin Nordbotten, Michael A. Celia, 2011 0 0