Manual

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Equations, properties, methods, etc.:

• Equations and parameters - Non-dimensionalisation, Navier-Stokes, Reynolds numbers.
• The PPE formulation - Pressure-Poisson Equation, and the influence matrix technique.
• Differential operators in cylindrical coordinates - grad, div, curl, Laplacian, etc.
• Symmetries of pipe flow - discrete and continuous symmetries.
• Method of slices - symmetry reduction, elimination of physically irrelevant spatial shifts.
• Newton-Krylov method - see non-problem specific code below.

Using the simulation code:

• Getting started - overview of files, setup, starting and ending a job.
• Tutorial - setup a job, basic monitoring and visualisation of outputs.
• Core implementation - Discretisation, PPE formulation, Predictor-Corrector, Code Structure.
• Parallel i/o - a brief note on parallel data access.
• Utilities - pre/post-processing, runtime processing and manipulations, Newton solver for pipe flow.

Non-problem specific codes

• These are designed for integration with any pre-existing code.
• File:Arnoldi.f - Krylov-subspace method for calculating eigenvalues of a matrix.
• File:GMRESm.f90 - Krylov-subspace method for solving the linear system Ax=b for x.
• File:NewtonHook.f90 - Newton-Krylov-Hookstep method for finding nonlinear solutions x of F(x)=0.