From 174d109e0c1a027a3899ed3686a8fbce772d71c7 Mon Sep 17 00:00:00 2001
From: Valeria Barra <valeriabarra21@gmail.com>
Date: Tue, 23 Aug 2022 13:06:28 -0700
Subject: [PATCH] Fix Zalesak FCT docstring and add it to the Docs

---
 docs/refs.bib                     |  7 +++++++
 docs/src/operators.md             |  1 +
 src/Operators/finitedifference.jl | 21 +++++++++++----------
 3 files changed, 19 insertions(+), 10 deletions(-)

diff --git a/docs/refs.bib b/docs/refs.bib
index 69857b5ee4..488dd8aa67 100644
--- a/docs/refs.bib
+++ b/docs/refs.bib
@@ -30,6 +30,13 @@ @article{BorisBook1973
   author = {Jay P Boris and David L Book}
 }
 
+@book{durran2010,
+  title={Numerical Methods for Fluid Dynamics},
+  author={Durran, Dale R},
+  year={2010},
+  publisher={Springer New York, NY}
+}
+
 @book{durran2013numerical,
   title={Numerical methods for wave equations in geophysical fluid dynamics},
   author={Durran, Dale R},
diff --git a/docs/src/operators.md b/docs/src/operators.md
index 39b572aa1a..b015822f16 100644
--- a/docs/src/operators.md
+++ b/docs/src/operators.md
@@ -68,6 +68,7 @@ WeightedInterpolateF2C
 UpwindBiasedProductC2F
 Upwind3rdOrderBiasedProductC2F
 FCTBorisBook
+FCTZalesak
 LeftBiasedC2F
 RightBiasedC2F
 LeftBiasedF2C
diff --git a/src/Operators/finitedifference.jl b/src/Operators/finitedifference.jl
index e0a3186415..44f56a757c 100644
--- a/src/Operators/finitedifference.jl
+++ b/src/Operators/finitedifference.jl
@@ -1463,20 +1463,20 @@ end
     U = FCTBorisBook(;boundaries)
     U.(v, x)
 
-Correct the flux using the flux-corrected transport formulation by Boris and Book
+Correct the flux using the flux-corrected transport formulation by Boris and Book [BorisBook1973](@cite).
+
 Input arguments:
 - a face-valued vector field `v`
 - a center-valued field `x`
 ```math
 Ac(v,x)[i] =
-  s[i] \\max \\left\\{0, \\min \\left[ |v[i] |, s[i] \\left( x[i+\\tfrac{3}{2}] - x[i+\\tfrac{1}{2}]  \\right) \\Delta z ,  s[i] \\left( x[i-\\tfrac{1}{2}] - x[i-\\tfrac{3}{2}]  \\right) \\Delta z \\right] \\right\\},
+  s[i] \\max \\left\\{0, \\min \\left[ |v[i] |, s[i] \\left( x[i+\\tfrac{3}{2}] - x[i+\\tfrac{1}{2}]  \\right) ,  s[i] \\left( x[i-\\tfrac{1}{2}] - x[i-\\tfrac{3}{2}]  \\right) \\right] \\right\\},
 ```
 where ``s[i] = +1`` if  `` v[i] \\geq 0`` and ``s[i] = -1`` if  `` v[i] \\leq 0``, and ``Ac`` represents the resulting corrected antidiffusive flux.
-This formulation is based on [BorisBook1973](@cite).
+This formulation is based on [BorisBook1973](@cite), as reported in [durran2010](@cite) section 5.4.1.
 
 Supported boundary conditions are:
-- [`FirstOrderOneSided(x₀)`](@ref): uses the first-order downwind reconstruction to compute `x` on the left boundary,
-and the first-order upwind reconstruction to compute `x` on the right boundary.
+- [`FirstOrderOneSided(x₀)`](@ref): uses the first-order downwind reconstruction to compute `x` on the left boundary, and the first-order upwind reconstruction to compute `x` on the right boundary.
 
 !!! note
     Similar to the [`Upwind3rdOrderBiasedProductC2F`](@ref) operator, these boundary conditions do not define the value at the actual boundary faces,
@@ -1593,19 +1593,20 @@ end
     U = FCTZalesak(;boundaries)
     U.(A, Φ, Φᵗᵈ)
 
-Correct the flux using the flux-corrected transport formulation by Zalesak
+Correct the flux using the flux-corrected transport formulation by Zalesak [zalesak1979fully](@cite).
+
 Input arguments:
 - a face-valued vector field `A`
 - a center-valued field `Φ`
 - a center-valued field `Φᵗᵈ`
 ```math
-Φ_j^{n+1} = Φ_j^{td} - \frac{dt}{dx}(C_{j+\frac{1}{2}}A_{j+\frac{1}{2}} - C_{j-\frac{1}{2}}A_{j-\frac{1}{2}})
+Φ_j^{n+1} = Φ_j^{td} - (C_{j+\\frac{1}{2}}A_{j+\\frac{1}{2}} - C_{j-\\frac{1}{2}}A_{j-\\frac{1}{2}})
 ```
-This stencil is based on [zalesak1979fully](@cite).
+This stencil is based on [zalesak1979fully](@cite), as reported in [durran2010](@cite) section 5.4.2, where ``C`` denotes
+the corrected antidiffusive flux.
 
 Supported boundary conditions are:
-- [`FirstOrderOneSided(x₀)`](@ref): uses the first-order downwind reconstruction to compute `x` on the left boundary,
-and the first-order upwind reconstruction to compute `x` on the right boundary.
+- [`FirstOrderOneSided(x₀)`](@ref): uses the first-order downwind reconstruction to compute `x` on the left boundary, and the first-order upwind reconstruction to compute `x` on the right boundary.
 
 !!! note
     Similar to the [`Upwind3rdOrderBiasedProductC2F`](@ref) operator, these boundary conditions do not define