feat: init the NS post.

src/bqn/ns.bqn

@@ -0,0 +1,5 @@
+cn ← {
+  _p ⇐ {(-´𝔽¨)⋈(+´𝔽¨)⟜⌽}
+  Cis ⇐ (⍉•math.Cos≍•math.Sin)¯π×↕⊸÷
+}
+FFT ← {𝕊⁼: ⋈⟜-´˘{≠÷˜·𝔽𝔾∘𝔽}𝕊𝕩; (1=≠)◶⟨(+∾-)⟜(⊢×cn._p˘cn.Cis∘≠)´(𝕊¨⊢⊔˜2|⊒˜), ⊢⟩𝕩}

src/index.org

@@ -36,5 +36,6 @@
 5. [[./si.org][Scheming a mise-en-abîme in BQN]]
 6. [[./aoc24.org][Coding in Advent]]
 7. [[./nn.org][The miniaturist's neural network]]
+8. [[./ns.org][Navier-Stokes simulator]]
 
 #+HTML: </div>

src/ns.org

@@ -0,0 +1,44 @@
+# -*- eval: (face-remap-add-relative 'default '(:family "BQN386 Unicode" :height 180)); -*-
+#+TITLE: Navier-Stokes simulator (WIP)
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="assets/style.css"/>
+#+HTML_HEAD: <link rel="icon" href="assets/favicon.ico" type="image/x-icon">
+#+HTML_HEAD: <style>
+#+HTML_HEAD: mjx-container[jax="CHTML"] {
+#+HTML_HEAD:   overflow-x: auto !important;
+#+HTML_HEAD: }
+#+HTML_HEAD: </style>
+
+** Foreword
+
+We want to solve the following [[https://en.wikipedia.org/wiki/Derivation_of_the_Navier%E2%80%93Stokes_equations][system]] of partial differential equations
+in two dimensions for an incompressible fluid, imposing periodic boundary conditions:
+
+\begin{equation*}
+  \begin{aligned}
+    \nabla \cdot \mathbf{q} &= 0,\\
+    \frac{\partial \mathbf{q}}{\partial t}
+    + \nabla \cdot (\mathbf{q} \otimes \mathbf{q}) &=
+    -\nabla p + \frac{1}{\text{Re}} \nabla^2 \mathbf{q},
+  \end{aligned}
+\end{equation*}
+
+** Simulator
+
+The numerical solution will be obtained using this zero-dependency BQN code:
+
+#+begin_src bqn :tangle bqn/ns.bqn :exports code
+  cn ← {
+    _p ⇐ {(-´𝔽¨)⋈(+´𝔽¨)⟜⌽}
+    Cis ⇐ (⍉•math.Cos≍•math.Sin)¯π×↕⊸÷
+  }
+  FFT ← {𝕊⁼: ⋈⟜-´˘{≠÷˜·𝔽𝔾∘𝔽}𝕊𝕩; (1=≠)◶⟨(+∾-)⟜(⊢×cn._p˘cn.Cis∘≠)´(𝕊¨⊢⊔˜2|⊒˜), ⊢⟩𝕩}
+#+end_src
+
+#+RESULTS:
+: (function block)
+
+#+BEGIN_EXPORT html
+  <div style="text-align: center; font-size: 2em; padding: 20px 0;">
+    <a href="https://panadestein.github.io/blog/" style="text-decoration: none;">⊑∘∞</a>
+  </div>
+#+END_EXPORT