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(-)
(limited to 'articles')
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
-
-
-
-
-
+
## Reaching down from the heavens
+
+
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