Video tutorials on modelling incompressible flow
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The Navier-Stokes equations (# 1, ~24 minutes, 25Mb)
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This first video sets the scene for the specialised videos.
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The Reynolds number (# 2, ~16 minutes, 71Mb)
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This video discusses nondimensionalisation of the Navier-Stokes equations
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The Stokes equations (# 3, ~22 minutes, 97Mb)-
This video discusses the Stokes equations (zero Reynolds number limit)
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The discretised Stokes equations (# 4, ~18 minutes, 85Mb)-
This video discusses the saddle-point system associated with discretised Stokes equations
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Vorticity-Streamfunction formulations (# 5, ~26 minutes, 81Mb)-
This video discusses alternative formulations of the Stokes equations
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Potential flow (# 6, ~16 minutes, 156Mb)-
This video discusses a classic simplification of the Navier-Stokes equations
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MAC discretization scheme | part I (# 7, ~22 minutes, 109Mb)-
This video discusses Marker and Cell discretization of the Stokes equations
MAC discretization scheme | part II (# 8, ~15 minutes, 55Mb)-
This video discusses Marker and Cell discretization of the Navier-Stokes equations
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The following videos are concerned with approximation of the incompressibility constraint
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Approximation issues | part I (# 9, ~22 minutes, 81Mb)-
This video discusses local stability of discretizations of the Stokes equations
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supplementary notes)
Approximation issues | part II (# 10, ~20 minutes, 64Mb)-
This video discusses inf-sup (global) stability of discretizations of the Stokes equations
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supplementary notes)
Approximation issues | part III (# 13, ~23 minutes, 220Mb)-
This video discusses the characterisation of the inf-sup stability constant
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supplementary notes)
Approximation issues | part IV (# 14, ~23 minutes, 122Mb)-
This video discusses issues associated with unstable discretization strategies
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supplementary notes)
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Taylor-Hood approximation | part I (# 11, ~28 minutes, 115Mb)-
This video discusses stability on rectangular and hexahedral grids ... using non-overlapping macroelements
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supplementary notes)
Taylor-Hood approximation | part II (# 12, ~20 minutes, 82Mb)-
This video discusses stability on unstructured grids ... using overlapping macroelements
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supplementary notes)
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Enhanced Taylor-Hood approximation | part I (# 15, ~19 minutes, 132Mb)-
This video discusses augmenting Taylor-Hood approximation to ensure local mass conservation
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supplementary notes)
Enhanced Taylor-Hood approximation | part II (# 16, ~18 minutes, 96Mb)-
This video discusses stability of enhanced Taylor-Hood approximation
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supplementary notes)
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Scott-Vogelius approximation (# 17, ~22 minutes, 73Mb)-
This video discusses refining Taylor-Hood approximation to ensure pointwise mass conservation
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supplementary notes)
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Pressure-robust approximation (# 18, ~27 minutes, 89Mb)-
This video discusses the importance of pressure-robust approximation in
the efficient solution of steady flow problems
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supplementary notes)
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