Merge #853 #909 #910

853: add special cases for projection from Covariant => Contravariant r=charleskawczynski a=simonbyrne



909: Fix differentiability of local element map r=simonbyrne a=simonbyrne

I was experimenting with `IntrinsicMap` and noticed some sign errors in the metric terms due to the non-differentiable extra branches for handling of signed zeros. This is a simpler and better approach.

- [X] Code follows the [style guidelines](https://clima.github.io/ClimateMachine.jl/latest/DevDocs/CodeStyle/) OR N/A.
- [X] Unit tests are included OR N/A.
- [X] Code is exercised in an integration test OR N/A.
- [X] Documentation has been added/updated OR N/A.


910: Fix Zalesak FCT docstring and add it to the Docs r=simonbyrne a=valeriabarra

This PR adds the Zalesak FCT operator to the docs since #887  did not include it. Plus some additional doc fixes and improvements.

- [x] Code follows the [style guidelines](https://clima.github.io/ClimateMachine.jl/latest/DevDocs/CodeStyle/) OR N/A.
- [x] Unit tests are included OR N/A.
- [x] Code is exercised in an integration test OR N/A.
- [x] Documentation has been added/updated OR N/A.


Co-authored-by: Simon Byrne <[email protected]>
Co-authored-by: Charles Kawczynski <[email protected]>
Co-authored-by: Valeria Barra <[email protected]>

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},

docs/src/operators.md

@@ -68,6 +68,7 @@ WeightedInterpolateF2C
 UpwindBiasedProductC2F
 Upwind3rdOrderBiasedProductC2F
 FCTBorisBook
+FCTZalesak
 LeftBiasedC2F
 RightBiasedC2F
 LeftBiasedF2C

src/Geometry/axistensors.jl

@@ -287,13 +287,16 @@ const Axis2TensorOrAdj{T, A, S} =
 
 # based on 1st dimension
 const Covariant2Tensor{T, A, S} =
-    Axis2Tensor{T, A, S} where {A <: Tuple{CovariantAxis, AbstractAxis}}
-const Contravariant2Tensor{T, A, S} =
-    Axis2Tensor{T, A, S} where {A <: Tuple{ContravariantAxis, AbstractAxis}}
+    Axis2Tensor{T, A, S} where {T, A <: Tuple{CovariantAxis, AbstractAxis}, S}
+const Contravariant2Tensor{T, A, S} = Axis2Tensor{
+    T,
+    A,
+    S,
+} where {T, A <: Tuple{ContravariantAxis, AbstractAxis}, S}
 const Cartesian2Tensor{T, A, S} =
-    Axis2Tensor{T, A, S} where {A <: Tuple{CartesianAxis, AbstractAxis}}
+    Axis2Tensor{T, A, S} where {T, A <: Tuple{CartesianAxis, AbstractAxis}, S}
 const Local2Tensor{T, A, S} =
-    Axis2Tensor{T, A, S} where {A <: Tuple{LocalAxis, AbstractAxis}}
+    Axis2Tensor{T, A, S} where {T, A <: Tuple{LocalAxis, AbstractAxis}, S}
 
 const CovariantTensor = Union{CovariantVector, Covariant2Tensor}
 const ContravariantTensor = Union{ContravariantVector, Contravariant2Tensor}
@@ -521,6 +524,9 @@ end
     x
 end
 
+#= Set `assert_exact_transform() = true` for debugging=#
+assert_exact_transform() = false
+
 @generated function _transform(
     ato::Ato,
     x::Axis2Tensor{T, Tuple{Afrom, A2}},
@@ -531,12 +537,14 @@ end
 } where {Ito, Ifrom, J, T}
     N = length(Ifrom)
     M = length(J)
-    errcond = false
-    for n in 1:N
-        i = Ifrom[n]
-        if i ∉ Ito
-            for m in 1:M
-                errcond = :($errcond || x[$n, $m] != zero(T))
+    if assert_exact_transform()
+        errcond = false
+        for n in 1:N
+            i = Ifrom[n]
+            if i ∉ Ito
+                for m in 1:M
+                    errcond = :($errcond || x[$n, $m] != zero(T))
+                end
             end
         end
     end
@@ -555,8 +563,10 @@ end
     end
     quote
         Base.@_propagate_inbounds_meta
-        if $errcond
-            throw(InexactError(:transform, Ato, x))
+        if assert_exact_transform()
+            if $errcond
+                throw(InexactError(:transform, Ato, x))
+            end
         end
         @inbounds Axis2Tensor(
             (ato, axes(x, 2)),
@@ -594,11 +604,11 @@ end
     ))
 end
 
-@inline transform(ato::CovariantAxis, v::CovariantTensor) = _transform(ato, v)
+@inline transform(ato::CovariantAxis, v::CovariantTensor) = _project(ato, v)
 @inline transform(ato::ContravariantAxis, v::ContravariantTensor) =
-    _transform(ato, v)
-@inline transform(ato::CartesianAxis, v::CartesianTensor) = _transform(ato, v)
-@inline transform(ato::LocalAxis, v::LocalTensor) = _transform(ato, v)
+    _project(ato, v)
+@inline transform(ato::CartesianAxis, v::CartesianTensor) = _project(ato, v)
+@inline transform(ato::LocalAxis, v::LocalTensor) = _project(ato, v)
 
 @inline project(ato::CovariantAxis, v::CovariantTensor) = _project(ato, v)
 @inline project(ato::ContravariantAxis, v::ContravariantTensor) =