From 77151351a406adb4f773f8163652e3c4e3cbd06b Mon Sep 17 00:00:00 2001 From: Adrian Kummerlaender Date: Thu, 20 Dec 2018 20:31:31 +0100 Subject: Add videos to CFD article --- ...2_fun_with_compute_shaders_and_fluid_dynamics.md | 21 +++++++-------------- 1 file 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 $p = c_s^2 \rho$ + -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 -![Pleasing snapshot of an artfully amplified implosion](https://static.kummerlaender.eu/media/boltzstern_1.jpg) - -![Pleasing snapshot of an artfully amplified implosion](https://static.kummerlaender.eu/media/boltzstern_2.jpg) - -![Pleasing snapshot of an artfully amplified implosion](https://static.kummerlaender.eu/media/boltzstern_3.jpg) + ## Reaching down from the heavens + + -- cgit v1.2.3