MEng Chemical Engineering / Course details

Year of entry: 2021

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Course unit details:Fundamentals of Numerical Methods & Simulation

Unit code CHEN40451 15 Level 4 Semester 1 Department of Chemical Engineering & Analytical Science No

Overview

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, oil recovery, heat extraction from the Earth. 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: ¿ Introduction to Flow Charts, how to design the pseudo-codes ¿ Introduction to syntax, commands and programming (self-study). ¿ Introduction to the partial differential equations (PDEs) commonly used for subsurface energy engineering ¿ Principals of Taylor expansion and how to discretise first, second and third order derivates ¿ Discretisation of elliptic and hyperbolic partial differential equations, ¿ Introduction to a computational problem; numerical domain, boundary and initial conditions, ¿ Introduction to Finite Difference and Finite Volume Schemes, ¿ Convergence and numerical stability,  ¿ Project on numerical modelling of an elliptic PDE for subsurface energy engineering. ¿ Project on numerical modelling of a hyperbolic PDE for subsurface energy engineering.

Aims

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.

Learning outcomes

ILO 1. Develop flowcharts to deconvolute a given complex engineering problem to different steps of required for numerical modelling.

ILO 2. Demonstrate capability to covert a pseudo-code to a computer program

ILO 3. Develop the mathematical framework for an engineering problem with correct boundary and initial conditions, and governing equations

ILO 4. Characterise the types of the partial differential equations for subsurface energy engineering with the associated numerical approach

ILO 5. Write the discretised form of a partial differential equation and describe the expected numerical errors and accuracy in their discretised equations

ILO 6. Solve numerically the elliptic and hyperbolic partial differential equations applicable to flow and transport in porous media

ILO 7. Work in a team to develop a group numerical project and collectively assess the key elements required for modelling a subsurface energy application

Teaching and learning methods

There will be delivered by a combination of lectures and computational laboratory delivered by blended teaching. The theoretical parts will be covered in the lectures and practical knowledge will be developed in practical sessions.

Assessment methods

 Assessment task Length Weighting within unit (if relevant) Continuous assessment - 30% Exam style assessment - 70%

All reading lists now must be managed through the library tool at: https://www.library.manchester.ac.uk/using-the-library/staff/reading-lists/

Study hours

Scheduled activity hours
Lectures 24
Tutorials 12
Independent study hours
Independent study 114

Teaching staff

Staff member Role
Vahid Joekar-Niasar Unit coordinator