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Industrial Mathematics Final Year Topic: Numerical Diffusion and Conservation in a One-Dimensional Transport Model

This Industrial Mathematics final year project compares transport discretisations using a known model pulse and conservation checks.

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Why choose this project topic?

A focused study of advection–diffusion error gives you a specific question in applied partial differential equations. It compares transport discretisations using a known model pulse and conservation checks. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.

How do spatial resolution and discretisation choices change the shape and mass of a transported model pulse?

Agree the apparatus or dataset, comparison range and feasible measurement schedule for advection–diffusion error with your supervisor.

Proposed project objectives

  1. 01Define the materials, variables and comparison conditions for advection–diffusion error.
  2. 02Specify the advection-diffusion equation, boundaries and a reference solution.
  3. 03Evaluate the measurements or model outputs in relation to this question: How do spatial resolution and discretisation choices change the shape and mass of a transported model pulse?

A suggested research approach

Specify the advection-diffusion equation, boundaries and a reference solution. Compare suitable numerical schemes at matched resolutions, distinguish artificial spreading from physical diffusion and track integrated mass over time. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.

What you will need

  • A documented transport equation and reference solution
  • Numerical discretisation tools
  • Mass, positivity and profile-error diagnostics

Keep your project scope clear

The model does not predict real contaminant concentrations without verified inputs, calibration and appropriate boundary conditions.

Industrial Mathematics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

  1. Chapter 1Introduction
  2. Chapter 2Literature Review
  3. Chapter 3Theory and Methodology
  4. Chapter 4Results and Applications
  5. Chapter 5Summary, Conclusion and Recommendations

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