diff --git a/examples/cahn_hilliard/README.md b/examples/cahn_hilliard/README.md
index 11552d371170e8184917058c461b43e2a353c6d5..1e0793215bafe3c963cd976dd85768253cdc1f17 100644
--- a/examples/cahn_hilliard/README.md
+++ b/examples/cahn_hilliard/README.md
@@ -45,7 +45,7 @@ with the concentration $c(x,t)$, the mobility coefficient $M$, and surface tensi
The domain $\Omega \subset \mathbb{R}^2$ is initialized with a concentration field
$c(x,t=0) = 0.42 + \zeta$, randomly perturbed by
noise $\zeta$ following a uniform distribution $\zeta \sim U(-0.02, 0.02)$.
-With time the concentration field evolves towards attaining mostly values near to $0$ or $1$ while
+Over time, the concentration field evolves towards attaining mostly values near to $0$ or $1$ while
conserving the total concentration. The model describes the separation of two immiscible fluids.
The fourth order PDE cannot be solved by a standard finite volume scheme. We therefore
diff --git a/examples/cahn_hilliard/doc/_intro.md b/examples/cahn_hilliard/doc/_intro.md
index 42f94f6c00ef5c09d5439112abc854ce91748f5a..ad6b4bcce751ed62ae82851c1811bd3b084fd658 100644
--- a/examples/cahn_hilliard/doc/_intro.md
+++ b/examples/cahn_hilliard/doc/_intro.md
@@ -43,7 +43,7 @@ with the concentration $c(x,t)$, the mobility coefficient $M$, and surface tensi
The domain $\Omega \subset \mathbb{R}^2$ is initialized with a concentration field
$c(x,t=0) = 0.42 + \zeta$, randomly perturbed by
noise $\zeta$ following a uniform distribution $\zeta \sim U(-0.02, 0.02)$.
-With time the concentration field evolves towards attaining mostly values near to $0$ or $1$ while
+Over time, the concentration field evolves towards attaining mostly values near to $0$ or $1$ while
conserving the total concentration. The model describes the separation of two immiscible fluids.
The fourth order PDE cannot be solved by a standard finite volume scheme. We therefore
diff --git a/examples/cahn_hilliard/doc/main.md b/examples/cahn_hilliard/doc/main.md
index 778b01e7616ba460060b8ff8eb9f0db9282f88f4..1d42334b80f602504e740832fbe363eae8c8b316 100644
--- a/examples/cahn_hilliard/doc/main.md
+++ b/examples/cahn_hilliard/doc/main.md
@@ -105,7 +105,7 @@ public:
In the `source` function, we implement the derivative of the free energy.
This demonstrates how parts of the local residual can be split into model specific
-parts and parts that might change from scenario to scenario.
+parts (see `CahnHilliardModelLocalResidual`) and parts that might change from scenario to scenario.
```cpp
template<class ElementVolumeVariables>
@@ -121,8 +121,8 @@ parts and parts that might change from scenario to scenario.
}
```
-For the boundary we choose boundary flux (or Neumann) conditions for all equations and on
-every part of the boundary, specifying zero flux everywhere for both equations.
+We choose boundary flux (or Neumann) conditions for all equations on the entire boundary,
+while specifying zero flux for both equations.
```cpp
BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
@@ -138,7 +138,7 @@ every part of the boundary, specifying zero flux everywhere for both equations.
The parameters interfaces are used in the local residual (see Part 1).
We can name this interface however we want as long as we adapt the calling site
-in the `LocalResidual` class in `model.hh`.
+in the `CahnHilliardModelLocalResidual` class in `model.hh`.
```cpp
Scalar mobility() const
diff --git a/examples/cahn_hilliard/doc/model.md b/examples/cahn_hilliard/doc/model.md
index 5d90744ef6254e260b8633731734bc38362a4e4a..3fdad2164fa0665bb227584c84646c1c55f07e61 100644
--- a/examples/cahn_hilliard/doc/model.md
+++ b/examples/cahn_hilliard/doc/model.md
@@ -183,14 +183,13 @@ the equation for the chemical potential does not have a storage term.
}
```
-**Flux term:** The function `computeFlux` computes the fluxes
-over a sub control volume faces, including the integration over
-the area of the face.
+**Flux term:** The function `computeFlux` computes the integrated
+fluxes over a sub control volume face.
```math
\begin{aligned}
-F_{K,\sigma,0} &= -M \sum_{B \in \mathcal{B}_K} \mu_{h,B} \nabla N_B \cdot\boldsymbol{n} \vert \sigma \vert \cr
-F_{K,\sigma,1} &= -\gamma \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\boldsymbol{n} \vert \sigma \vert
+F_{K,\sigma,0} &= -M \vert \sigma \vert \sum_{B \in \mathcal{B}_K} \mu_{h,B} \nabla N_B \cdot\boldsymbol{n} \cr
+F_{K,\sigma,1} &= -\gamma \vert \sigma \vert \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\boldsymbol{n}
\end{aligned}
````
@@ -212,7 +211,7 @@ F_{K,\sigma,1} &= -\gamma \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\bo
for (const auto& scv : scvs(fvGeometry))
{
const auto& volVars = elemVolVars[scv];
- // v.axpy(a, w) means v <- v + a*w
+ // v.axpy(a, w) means v += a*w
gradConcentration.axpy(
volVars.concentration(),
fluxVarCache.gradN(scv.indexInElement())
@@ -236,7 +235,7 @@ F_{K,\sigma,1} &= -\gamma \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\bo
}
```
-**Source term:** The function `computeSource` computes the sources terms for a sub control volume.
+**Source term:** The function `computeSource` computes the source terms for a sub control volume.
We implement a model-specific source term for the chemical potential equation before
deferring further implementation to the problem where we add the derivative of the free
energy.
@@ -285,7 +284,6 @@ struct LocalResidual<TypeTag, TTag::CahnHilliardModel>
{ using type = CahnHilliardModelLocalResidual<TypeTag>; };
```
-The default scalar type is double.
We compute with double precision floating point numbers.
```cpp
@@ -296,7 +294,7 @@ struct Scalar<TypeTag, TTag::CahnHilliardModel>
The model traits specify some information about our equation system.
Here we have two equations. The indices allow to access primary variables
-and equations with a named indices.
+and equations with named indices.
```cpp
template<class TypeTag>
@@ -319,7 +317,8 @@ struct ModelTraits<TypeTag, TTag::CahnHilliardModel>
```
The primary variable vector has entries of type `Scalar` and is
-as large as the number of equations (here 2) but we keep it general.
+as large as the number of equations (here 2) but we keep it general
+here by obtaining the number of equations from the `ModelTraits`.
```cpp
template<class TypeTag>
diff --git a/examples/cahn_hilliard/main.cc b/examples/cahn_hilliard/main.cc
index 4cf109f366adb2f08fa206db84102c995001f3e0..6ddde40f8b2aaaf10460f5fa2c18c267a815a2fc 100644
--- a/examples/cahn_hilliard/main.cc
+++ b/examples/cahn_hilliard/main.cc
@@ -85,7 +85,7 @@ public:
// In the `source` function, we implement the derivative of the free energy.
// This demonstrates how parts of the local residual can be split into model specific
- // parts and parts that might change from scenario to scenario.
+ // parts (see `CahnHilliardModelLocalResidual`) and parts that might change from scenario to scenario.
template<class ElementVolumeVariables>
NumEqVector source(const Element &element,
const FVElementGeometry& fvGeometry,
@@ -98,8 +98,8 @@ public:
return values;
}
- // For the boundary we choose boundary flux (or Neumann) conditions for all equations and on
- // every part of the boundary, specifying zero flux everywhere for both equations.
+ // We choose boundary flux (or Neumann) conditions for all equations on the entire boundary,
+ // while specifying zero flux for both equations.
// [[codeblock]]
BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
{
@@ -114,7 +114,7 @@ public:
// The parameters interfaces are used in the local residual (see Part 1).
// We can name this interface however we want as long as we adapt the calling site
- // in the `LocalResidual` class in `model.hh`.
+ // in the `CahnHilliardModelLocalResidual` class in `model.hh`.
// [[codeblock]]
Scalar mobility() const
{ return mobility_; }
diff --git a/examples/cahn_hilliard/model.hh b/examples/cahn_hilliard/model.hh
index 2b765ce3c0194c24a6d63bd138bfcb160d99a59a..80470f9d42cbe9c90b277f5afb0151d8870883f0 100644
--- a/examples/cahn_hilliard/model.hh
+++ b/examples/cahn_hilliard/model.hh
@@ -181,14 +181,13 @@ public:
}
// [[/codeblock]]
- // **Flux term:** The function `computeFlux` computes the fluxes
- // over a sub control volume faces, including the integration over
- // the area of the face.
+ // **Flux term:** The function `computeFlux` computes the integrated
+ // fluxes over a sub control volume face.
//
// ```math
// \begin{aligned}
- // F_{K,\sigma,0} &= -M \sum_{B \in \mathcal{B}_K} \mu_{h,B} \nabla N_B \cdot\boldsymbol{n} \vert \sigma \vert \cr
- // F_{K,\sigma,1} &= -\gamma \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\boldsymbol{n} \vert \sigma \vert
+ // F_{K,\sigma,0} &= -M \vert \sigma \vert \sum_{B \in \mathcal{B}_K} \mu_{h,B} \nabla N_B \cdot\boldsymbol{n} \cr
+ // F_{K,\sigma,1} &= -\gamma \vert \sigma \vert \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\boldsymbol{n}
// \end{aligned}
// ````
//
@@ -209,7 +208,7 @@ public:
for (const auto& scv : scvs(fvGeometry))
{
const auto& volVars = elemVolVars[scv];
- // v.axpy(a, w) means v <- v + a*w
+ // v.axpy(a, w) means v += a*w
gradConcentration.axpy(
volVars.concentration(),
fluxVarCache.gradN(scv.indexInElement())
@@ -233,7 +232,7 @@ public:
}
// [[/codeblock]]
- // **Source term:** The function `computeSource` computes the sources terms for a sub control volume.
+ // **Source term:** The function `computeSource` computes the source terms for a sub control volume.
// We implement a model-specific source term for the chemical potential equation before
// deferring further implementation to the problem where we add the derivative of the free
// energy.
@@ -270,7 +269,6 @@ template<class TypeTag>
struct LocalResidual<TypeTag, TTag::CahnHilliardModel>
{ using type = CahnHilliardModelLocalResidual<TypeTag>; };
-// The default scalar type is double.
// We compute with double precision floating point numbers.
template<class TypeTag>
struct Scalar<TypeTag, TTag::CahnHilliardModel>
@@ -278,7 +276,7 @@ struct Scalar<TypeTag, TTag::CahnHilliardModel>
// The model traits specify some information about our equation system.
// Here we have two equations. The indices allow to access primary variables
-// and equations with a named indices.
+// and equations with named indices.
template<class TypeTag>
struct ModelTraits<TypeTag, TTag::CahnHilliardModel>
{
@@ -298,7 +296,8 @@ struct ModelTraits<TypeTag, TTag::CahnHilliardModel>
};
// The primary variable vector has entries of type `Scalar` and is
-// as large as the number of equations (here 2) but we keep it general.
+// as large as the number of equations (here 2) but we keep it general
+// here by obtaining the number of equations from the `ModelTraits`.
template<class TypeTag>
struct PrimaryVariables<TypeTag, TTag::CahnHilliardModel>
{