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| author | Adrian Kummerlaender | 2018-12-20 20:31:31 +0100 |
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| committer | Adrian Kummerlaender | 2018-12-20 20:31:31 +0100 |
| commit | 77151351a406adb4f773f8163652e3c4e3cbd06b (patch) | |
| tree | 76a263aef9eb6de9b486e3414580c48b49ce5448 /articles | |
| parent | a30a3fb1d55c3ef390e21f62429513d6544491dd (diff) | |
| download | blog_content-77151351a406adb4f773f8163652e3c4e3cbd06b.tar blog_content-77151351a406adb4f773f8163652e3c4e3cbd06b.tar.gz blog_content-77151351a406adb4f773f8163652e3c4e3cbd06b.tar.bz2 blog_content-77151351a406adb4f773f8163652e3c4e3cbd06b.tar.lz blog_content-77151351a406adb4f773f8163652e3c4e3cbd06b.tar.xz blog_content-77151351a406adb4f773f8163652e3c4e3cbd06b.tar.zst blog_content-77151351a406adb4f773f8163652e3c4e3cbd06b.zip | |
Add videos to CFD article
Diffstat (limited to 'articles')
| -rw-r--r-- | articles/2018-12-22_fun_with_compute_shaders_and_fluid_dynamics.md | 21 |
1 files changed, 7 insertions, 14 deletions
diff --git a/articles/2018-12-22_fun_with_compute_shaders_and_fluid_dynamics.md b/articles/2018-12-22_fun_with_compute_shaders_and_fluid_dynamics.md index 6c70270..bb0d6c7 100644 --- a/articles/2018-12-22_fun_with_compute_shaders_and_fluid_dynamics.md +++ b/articles/2018-12-22_fun_with_compute_shaders_and_fluid_dynamics.md @@ -1,16 +1,11 @@ # Fun with compute shaders and fluid dynamics -## First for some theory… - -What we want (Navier-Stokes): - -$$\begin{aligned} \partial_t \rho + \nabla \cdot (\rho u) &= 0 \\ \partial_t u + (u \cdot \nabla) u &= -\frac{1}{\rho} \nabla p + 2\nu\nabla \cdot (\mathrm{S})\end{aligned}$$ - -Pressure $p = c_s^2 \rho$ +<video controls="" preload="metadata" loop="true" poster="https://static.kummerlaender.eu/media/classical_explosion.poster.jpg"><source src="https://static.kummerlaender.eu/media/classical_explosion.teaser.mp4" type="video/mp4"/></video> -Kinetic viscosity: $\nu = c_s^2 \tau$ +## First for some theory… -Tensor: $\mathrm{S} = \frac{1}{2} (\nabla u + (\nabla u)^\top)$ +The behaviour of weakly compressible fluid flows -- i.e. non-supersonic flows where the compressibility of the flowing fluid plays a small but _non-central_ role -- is usually modelled by the weakly compressible Navier-Stokes equations which relate density $\rho$, pressure $p$, viscosity $\nu$ and speed $u$ to each other: +$$\begin{aligned} \partial_t \rho + \nabla \cdot (\rho u) &= 0 \\ \partial_t u + (u \cdot \nabla) u &= -\frac{1}{\rho} \nabla p + 2\nu\nabla \cdot \left(\frac{1}{2} (\nabla u + (\nabla u)^\top)\right)\end{aligned}$$ What we use (Boltzmann equilibrium): @@ -126,10 +121,8 @@ void main() { ## Visuals - - - - - +<video controls="" preload="metadata" loop="true" poster="https://static.kummerlaender.eu/media/boltzstern_1.jpg"><source src="https://static.kummerlaender.eu/media/boltzstern.mp4" type="video/mp4"/></video> ## Reaching down from the heavens + +<video controls="" preload="metadata" loop="true" poster="https://static.kummerlaender.eu/media/interactive_boltzmann_256.poster.jpg"><source src="https://static.kummerlaender.eu/media/interactive_boltzmann_256.mp4" type="video/mp4"/></video> |