[mod] misc

NaokiHori · May 22, 2024 · 06abc31 · 06abc31
1 parent 0bc3256
commit 06abc31
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Showing 23 changed files with 653 additions and 865 deletions.
diff --git a/docs/source/conf_params/mathjax_macro/momentum.py b/docs/source/conf_params/mathjax_macro/momentum.py
@@ -11,29 +11,23 @@ def add(macros):
     macros["momadvr"] = [
             (
                 "-"
-                "\\frac{1}{J}"
-                "\\frac{J}{h_{\\gr}}"
-                "\\ur"
+                "\\frac{\\ur}{h_{\\gr}}"
                 "\\pder{u_{#1}}{\\gr}"
             ),
             1
     ]
     macros["momadvt"] = [
             (
                 "-"
-                "\\frac{1}{J}"
-                "\\frac{J}{h_{\\gt}}"
-                "\\ut"
+                "\\frac{\\ut}{h_{\\gt}}"
                 "\\pder{u_{#1}}{\\gt}"
             ),
             1
     ]
     macros["momadvz"] = [
             (
                 "-"
-                "\\frac{1}{J}"
-                "\\frac{J}{h_{\\gz}}"
-                "\\uz"
+                "\\frac{\\uz}{h_{\\gz}}"
                 "\\pder{u_{#1}}{\\gz}"
             ),
             1

diff --git a/docs/source/discretisation/momentum/r/diffusion.rst b/docs/source/discretisation/momentum/r/diffusion.rst
@@ -15,6 +15,11 @@ Radial derivative
    \lrr
    +
    \lrr
+   \approx
+   2
+   \left(
+      \dlrr
+   \right)
 
 .. myliteralinclude:: /../../src/fluid/integrate/ux.c
    :language: c
@@ -24,23 +29,19 @@ Radial derivative
    :language: c
    :tag: second-order derivative in x
 
-********************
-Azimuthal derivative
-********************
+***********************************
+Azimuthal derivative, diagonal part
+***********************************
 
 .. math::
 
    \dmomdif{\vt}{\vr}
 
-=============
-Diagonal term
-=============
-
-Part of
-
 .. math::
 
    \ltr
+   \approx
+   \dltr
 
 .. myliteralinclude:: /../../src/fluid/integrate/ux.c
    :language: c
@@ -50,41 +51,41 @@ Part of
    :language: c
    :tag: second-order derivative in y
 
-=================
-Non-diagonal term
-=================
-
-Rest of
+***************************************
+Azimuthal derivative, non-diagonal part
+***************************************
 
 .. math::
 
-   \ltr
-
-and
+   \dmomdif{\vt}{\vr}
 
 .. math::
 
+   \ltr
+   +
    \lrt
+   \approx
+   \dltr
+   +
+   \dlrt
 
 .. myliteralinclude:: /../../src/fluid/integrate/ux.c
    :language: c
    :tag: diffusion in y, 1
 
-****************
-Axial derivative
-****************
+*******************************
+Axial derivative, diagonal part
+*******************************
 
 .. math::
 
    \dmomdif{\vz}{\vr}
 
-=============
-Diagonal term
-=============
-
 .. math::
 
    \lzr
+   \approx
+   \dlzr
 
 .. myliteralinclude:: /../../src/fluid/integrate/ux.c
    :language: c
@@ -94,13 +95,19 @@ Diagonal term
    :language: c
    :tag: second-order derivative in z
 
-=================
-Non-diagonal term
-=================
+***********************************
+Axial derivative, non-diagonal part
+***********************************
+
+.. math::
+
+   \dmomdif{\vz}{\vr}
 
 .. math::
 
    \lrz
+   \approx
+   \dlrz
 
 .. myliteralinclude:: /../../src/fluid/integrate/ux.c
    :language: c
@@ -119,6 +126,11 @@ Additional term
    \ltt
    +
    \ltt
+   \approx
+   2
+   \left\{
+      \dltt
+   \right\}
 
 .. myliteralinclude:: /../../src/fluid/integrate/ux.c
    :language: c

diff --git a/docs/source/discretisation/momentum/t/diffusion.rst b/docs/source/discretisation/momentum/t/diffusion.rst
@@ -2,21 +2,19 @@
 Diffusion
 #########
 
-*****************
-Radial derivative
-*****************
+********************************
+Radial derivative, diagonal part
+********************************
 
 .. math::
 
    \dmomdif{\vr}{\vt}
 
-=============
-Diagonal term
-=============
-
 .. math::
 
    \lrt
+   \approx
+   \dlrt
 
 .. myliteralinclude:: /../../src/fluid/integrate/uy.c
    :language: c
@@ -26,37 +24,42 @@ Diagonal term
    :language: c
    :tag: second-order derivative in x
 
-=================
-Non-diagonal term
-=================
+************************************
+Radial derivative, non-diagonal part
+************************************
+
+.. math::
+
+   \dmomdif{\vr}{\vt}
 
 .. math::
 
    \ltr
+   \approx
+   \dltr
 
 .. myliteralinclude:: /../../src/fluid/integrate/uy.c
    :language: c
    :tag: diffusion in x, 1
 
-********************
-Azimuthal derivative
-********************
+***********************************
+Azimuthal derivative, diagonal part
+***********************************
 
 .. math::
 
    \dmomdif{\vt}{\vt}
 
-=============
-Diagonal term
-=============
-
-Part of
-
 .. math::
 
    \ltt
    +
    \ltt
+   \approx
+   2
+   \left\{
+      \dltt
+   \right\}
 
 .. myliteralinclude:: /../../src/fluid/integrate/uy.c
    :language: c
@@ -66,37 +69,42 @@ Part of
    :language: c
    :tag: second-order derivative in y
 
-=================
-Non-diagonal term
-=================
+***************************************
+Azimuthal derivative, non-diagonal part
+***************************************
+
+.. math::
 
-Rest of
+   \dmomdif{\vt}{\vt}
 
 .. math::
 
    \ltt
    +
    \ltt
+   \approx
+   2
+   \left\{
+      \dltt
+   \right\}
 
 .. myliteralinclude:: /../../src/fluid/integrate/uy.c
    :language: c
    :tag: diffusion in y, 1
 
-****************
-Axial derivative
-****************
+*******************************
+Axial derivative, diagonal term
+*******************************
 
 .. math::
 
    \dmomdif{\vz}{\vt}
 
-=============
-Diagonal term
-=============
-
 .. math::
 
    \lzt
+   \approx
+   \dlzt
 
 .. myliteralinclude:: /../../src/fluid/integrate/uy.c
    :language: c
@@ -106,13 +114,19 @@ Diagonal term
    :language: c
    :tag: second-order derivative in z
 
-=================
-Non-diagonal term
-=================
+***********************************
+Axial derivative, non-diagonal term
+***********************************
+
+.. math::
+
+   \dmomdif{\vz}{\vt}
 
 .. math::
 
    \ltz
+   \approx
+   \dlzt
 
 .. myliteralinclude:: /../../src/fluid/integrate/uy.c
    :language: c
@@ -131,6 +145,10 @@ Additional term
    \lrt
    +
    \ltr
+   \approx
+   \dlrt
+   +
+   \dltr
 
 .. myliteralinclude:: /../../src/fluid/integrate/uy.c
    :language: c