AMPS I — Term Project Topics
Choose one topic (A–F) or propose your own · proposal due before Week 9 · report and talk in Week 16
How to choose
Six reactor-engineering topics, each a coupled flow–transport–reaction problem that combines several weeks of this course. You may also propose your own topic from your research (the Week 8 example: a cooling fin with k(T)). Every topic, including your own, is graded the same way (week16/W16_final_project.html): weak form, analysis, verification (MMS and a benchmark), results, LLM workflow.
| Topic | Tier | Physics | Course weeks used | New for you | |
|---|---|---|---|---|---|
| A | PEM fuel cell | standard | Brinkman flow (channel + porous GDL), O₂ transport, Butler–Volmer catalyst boundary | 6 (Robin BC), 11–12 (Stokes, Darcy), 13 (SUPG) | Brinkman equation, electrode kinetics |
| B | Packed-bed runaway | standard | Darcy flow, coupled (c,T) with Arrhenius kinetics, Robin wall cooling | 8–9 (Newton, continuation), 12 (Darcy), 13 (SUPG) | stiff exponential nonlinearity |
| C | Buoyant vertical bed | advanced | B + Boussinesq buoyancy feeding back into a Brinkman flow, time dependent | B + 10 (θ-method), 11, 14 (splitting) | two-way coupling, segregated iteration |
| D | Nernst–Planck | advanced | ion migration, electroneutrality, potential equation, coupled Butler–Volmer | 8–9, 11 (null spaces), 13 | migration, solution-dependent conductivity |
| E | Ignition–extinction (PAC) | advanced | B + pseudo-arclength continuation through folds, stability eigenvalues | B + 9, 15 (continuation) | bordering algorithm, eigenvalue stability |
| F | Catalyst map (adjoint) | standard | advection–diffusion–reaction forward model; PDE-constrained inverse problem for a spatially varying rate k(\mathbf x) | 5–7 (MMS, rates), 13 | adjoint gradients (dolfinx-adjoint), regularisation, optimisation |
Standard topics have a well-defined required part and leave room for stretch goals. Advanced topics build on a standard one (C and E on B, D on A’s electrode kinetics) — start them only if you are comfortable with Weeks 8–9 and 11–13. Each topic page lists required tasks, the verification that is specific to the topic, stretch goals, and milestones.
What every topic must contain
- Weak form of the full model with spaces, essential/natural conditions, and the nonlinear residual (or the reason the problem is linear).
- Analysis: which theorem covers the (linearised) problem, its constants, and where it can fail for your parameters (e.g. Péclet number, Arrhenius stiffness, loss of coercivity).
- Verification: an MMS convergence study with predicted rates on at least four meshes, and the topic’s own physical check (listed on each page), and
-np 1=-np 2. - Results: the topic’s design output, mesh-independent.
- LLM workflow with at least three concrete errors found and how.
Units: all topics use lumped, dimensionless parameter values. State the dimensionless groups (Péclet, Damköhler, …) that your values correspond to.
Choosing and claiming
- Write your choice and a two-line plan in the proposal (
week08/W08_project_proposal.ipynb, Section 1). At most three students per topic; topics are assigned in the order the proposals arrive. Students on the same topic must not share code (syllabus, Academic Integrity). - Own topic: it must be nonlinear or a flow problem and must allow an MMS study and one independent physical check.
- Bonus (+2 points,
W16_final_project.html§5): an adjoint-based inverse problem on top of topics A–E or your own topic. For topic F the inverse problem is the project itself; F’s bonus is its design-optimisation stretch goal instead.
Sources
Background reading is listed on each topic page.