ACSE 2: Modelling Dynamical Processes¶
Module Lead: Prof. Saskia Goes
Staff: Prof. Saskia Goes; Prof. Matthew Piggott; Prof. Stephen Neethling
Course Description¶
This module introduces the essential mathematics and physics for modelling how substances flow and deform. This will underpin both programming projects to solve simple heat and mass transfer problems and applied computational modelling projects where complex computer models are used to simulate the dynamics of fluids and/or solids.
The module will have two parts:
Part A will recap/introduce the fundamentals mathematics of computational modelling
Part B will consider the fundamental quantities and equations governing the dynamics of deformation, and will consider the application to several classic flow/deformation problems including practical exercises.
Part A of the module will cover the following topics:
Mathematical essentials for modelling dynamical processes, including algorithms, accuracy, convergence and stability
Linear Algebra, including matrices, eigenvalues and simple numerical algorithms such as
Gaussian elimination
Ordinary differential equations, including standard analytical solution methods and simple numerical algorithms
Partial differential equations, including standard solution methods and simple numerical algorithms
Part B of the module will cover the following topics:
Vector and tensor calculus as used in continuum mechanics
Kinematics of continuous media, including material vs spatial descriptions and tensor strain measures
Stress principles, including the Cauchy stress tensor, and various tensor stress measures.
Conservation laws, simple derivation of the conservation laws of mass, momentum and energy, and introduction to constitutive equations describing material response.
Potential flow: Laplace’s equation, examples and numerical solution methods
Fluid flow in simple geometries and solution methods
Basic solutions to the wave equation and examples.
Reading List¶
An Introduction to Continuum Mechanics, J. N. Reddy, Cambridge University Press, ISBN13 9781139178952, https://doi.org/10.1017/CBO9781139178952 (recommended)
Principles of Continuum Mechanics: A Study of Conservation Principles with Applications, J.N. Reddy, Cambridge University Press, ISBN13 9780511763212, https://doi.org/10.1017/CBO9780511763212
Introduction to Continuum Mechanics, W. M. Lai, D. Rubin and E. Krempl
Introduction to Applied Linear Algebra, Stephen Boyd and Lieven Vandenberghe