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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> |