Modern chemical engineering involves the use of a wide range of software tools to design, operate, and optimise chemical processes and their constituent unit operations as well as predicting the properties of pure substances and mixtures. Students therefore require a thorough understanding of the computational techniques that underpin the capabilities of such software. This understanding will allow students to use existing software most effectively and develop bespoke computational models for systems they need to analyse. Students will apply contemporary commercial and open-source software to research questions that they select, focusing on applications of computational fluid dynamics (CFD) and molecular simulation.

1. Systems of linear and non-linear equations a. Direct and iterative techniques b. Eigenvalue problems for linear and linearized systems 2. Ordinary differential equations (ODEs) and systems of ODEs a. Methods for initial and boundary value problems b. Implicit and explicit discretisations c. Stability d. Convergence 3. Optimisation a. Linear programming and gradient descent 4. Partial differential equations a. Finite difference, finite volume, finite element and spectral techniques 5. Applications of Computational Fluid Dynamics (CFD) and Molecular Modelling a. Coupled heat and mass transfer b. Multiphase flows c. Phonons and vibrational spectra of molecular systems

On successful completion of this module, students will be able to: • Use and describe the characteristics of common methods for solving systems of linear and non-linear equations • Use and describe the characteristics of common methods for solving systems of coupled ordinary differential equations • Use and describe the characteristics of common methods for numerical optimisation • Use and describe the characteristics of numerical methods to solve partial differential equations, with an emphasis on those that are relevant to modelling of transport phenomena • Describe contemporary techniques for modelling multiphase flows and use these techniques as they are provided in existing software • Apply molecular modelling methods to computationally predict vibrational spectra • Apply computational fluid dynamics and molecular modelling software to research questions • Make appropriate assumptions and simplifications when modelling chemical systems • Critically evaluate published research that involves numerical solutions, in particular computational fluid dynamics and molecular modelling simulations

On successful completion of this module, students will be able to: • Develop a critical attitude towards the capabilities and limitations of numerical solutions to mathematical models of chemical processes and phenomena

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The module will be taught via formal lectures, tutorials and computer lab sessions. The theory will be presented in lectures, and students will learn to use simulation software during the lab sessions. The main assessments are two projects in which the students will apply CFD and molecular modelling to topics of their choice that align with their research projects. Students will also complete coursework on the theory of numerical methods for chemical engineering problems. The theoretical content of the module is designed to develop students' fundamental understanding of computational techniques to enhance their agility in responding to open-ended engineering problems. The coursework also develops students' communication, collaboration, and problem-solving skills, as well as their resilience, creativity, and professionalism. As computational modelling is a rapidly evolving field, recent research results will be directly included in the lectures. Students will also review the literature and use research results in their coursework.