From a153d6556efbd3da8c12eafe193e462539f954a7 Mon Sep 17 00:00:00 2001
From: leonidas <leon.keim@googlemail.com>
Date: Fri, 27 Oct 2023 14:12:33 +0200
Subject: [PATCH] Change grad and div to symbolic nabla notation
---
dumux/flux/darcyslaw.hh | 6 +++---
dumux/flux/fickslaw.hh | 4 ++--
dumux/flux/fourierslaw.hh | 2 +-
dumux/flux/fourierslawnonequilibrium.hh | 4 ++--
dumux/flux/maxwellstefanslaw.hh | 2 +-
dumux/freeflow/compositional/navierstokesncmodel.hh | 4 ++--
dumux/freeflow/navierstokes/energy/model.hh | 2 +-
dumux/freeflow/nonisothermal/model.hh | 2 +-
.../fluidmatrixinteractions/porositydeformation.hh | 6 +++---
dumux/material/fluidsystems/3pimmiscible.hh | 2 +-
dumux/material/fluidsystems/base.hh | 4 ++--
dumux/material/fluidsystems/brineco2.hh | 2 +-
dumux/porenetwork/solidenergy/model.hh | 2 +-
dumux/porousmediumflow/1p/model.hh | 4 ++--
dumux/porousmediumflow/1pnc/model.hh | 8 ++++----
dumux/porousmediumflow/1pncmin/model.hh | 6 +++---
dumux/porousmediumflow/2p/model.hh | 4 ++--
dumux/porousmediumflow/2p1c/model.hh | 4 ++--
dumux/porousmediumflow/2p2c/model.hh | 8 ++++----
dumux/porousmediumflow/2pnc/model.hh | 6 +++---
dumux/porousmediumflow/2pncmin/model.hh | 6 +++---
dumux/porousmediumflow/3p/model.hh | 4 ++--
dumux/porousmediumflow/3p3c/model.hh | 8 ++++----
dumux/porousmediumflow/3pwateroil/model.hh | 8 ++++----
dumux/porousmediumflow/nonisothermal/model.hh | 6 +++---
dumux/porousmediumflow/richards/model.hh | 8 ++++----
dumux/porousmediumflow/richardsextended/model.hh | 10 +++++-----
dumux/porousmediumflow/richardsnc/model.hh | 6 +++---
dumux/porousmediumflow/solidenergy/model.hh | 2 +-
dumux/porousmediumflow/tracer/model.hh | 4 ++--
30 files changed, 72 insertions(+), 72 deletions(-)
diff --git a/dumux/flux/darcyslaw.hh b/dumux/flux/darcyslaw.hh
index 42d8762e30..22c6a33642 100644
--- a/dumux/flux/darcyslaw.hh
+++ b/dumux/flux/darcyslaw.hh
@@ -11,19 +11,19 @@
*
* Darcy's law describes the advective flux in porous media on the macro-scale and is valid in the creeping flow regime (Reynolds number << 1, Forchheimer extensions is also implemented->see forcheimerslaw.hh).
* The advective flux characterizes the bulk flow for each fluid phase including all components in case of compositional flow.
- * It is driven by the potential gradient \f$\textbf{grad}\, p - \varrho {\textbf g}\f$,
+ * It is driven by the potential gradient \f$\nabla p - \varrho {\textbf g}\f$,
* accounting for both pressure-driven and gravitationally-driven flow.
* The velocity is proportional to the potential gradient with the proportional factor \f$\frac{\textbf K}{\mu}\f$,
* including the intrinsic permeability of the porous medium, and the viscosity µ of the fluid phase. For one-phase flow it is:
* \f[
* v = - \frac{\mathbf K}{\mu}
- * \left(\textbf{grad}\, p - \varrho {\mathbf g} \right)
+ * \left(\nabla p - \varrho {\mathbf g} \right)
* \f]
* This equation can be extended to calculate the velocity \f$v_\alpha\f$ of phase \f$\alpha\f$ in the case of multi-phase
* flow by introducing a relative permeability \f$k_{r\alpha}\f$ restricting flow in the presence of other phases:
* \f[
* v_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K}
- * \left(\text{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right)
+ * \left(\nabla p_\alpha - \varrho_{\alpha} \mathbf{g} \right)
* \f]
*
* Darcy's law is specialized for different discretization schemes.
diff --git a/dumux/flux/fickslaw.hh b/dumux/flux/fickslaw.hh
index bd8c48b1c9..cfcf1e103f 100644
--- a/dumux/flux/fickslaw.hh
+++ b/dumux/flux/fickslaw.hh
@@ -15,14 +15,14 @@
*
* \n
* \f[
- * \mathbf{j}_{d} = - \varrho D_m \textbf{grad}\, X
+ * \mathbf{j}_{d} = - \varrho D_m \nabla X
* \f]
* \n
*
* Extending this to multi-phase, multi-component systems, Fick's law can be expressed as follows:
* \n
* \f[
- * \mathbf{j}_{d,\alpha}^\kappa = - \varrho_\alpha D_\alpha^\kappa \textbf{grad}\, X_\alpha^\kappa
+ * \mathbf{j}_{d,\alpha}^\kappa = - \varrho_\alpha D_\alpha^\kappa \nabla X_\alpha^\kappa
* \f]
* \n
*
diff --git a/dumux/flux/fourierslaw.hh b/dumux/flux/fourierslaw.hh
index 798e5856db..53ad87b0b5 100644
--- a/dumux/flux/fourierslaw.hh
+++ b/dumux/flux/fourierslaw.hh
@@ -14,7 +14,7 @@
* The flux is calculated as:\n
* \n
* \f[
- * \textbf{j}_{heat} = - \lambda \; \textbf{grad}\, T
+ * \textbf{j}_{heat} = - \lambda \; \nabla T
* \f]
* \n
* \n
diff --git a/dumux/flux/fourierslawnonequilibrium.hh b/dumux/flux/fourierslawnonequilibrium.hh
index bec4e9d9a3..e12815e184 100644
--- a/dumux/flux/fourierslawnonequilibrium.hh
+++ b/dumux/flux/fourierslawnonequilibrium.hh
@@ -10,12 +10,12 @@
* \brief Diffusive heat flux according to non-equilibrium Fourier's law
*
* This law is based on the general form of Fourier's law which describes the diffusive
- * heat flux as proportional to a temperature gradient \f$\textbf{grad}\, T_\alpha \f$.
+ * heat flux as proportional to a temperature gradient \f$\nabla T_\alpha \f$.
* In contrast to the general form, a local thermodynamic equilibrium is not assumed.
* Thus, the heat flux for the different phases \f$\alpha \f$ needs to be solved.
* \n
* \f[
- * \textbf{j}_{heat,\alpha} = - \lambda_\alpha \; \textbf{grad}\, T_\alpha
+ * \textbf{j}_{heat,\alpha} = - \lambda_\alpha \; \nabla T_\alpha
* \f]
* \n
* With \f$\lambda_\alpha \f$ as the thermal conductivity for either a solid, liquid or
diff --git a/dumux/flux/maxwellstefanslaw.hh b/dumux/flux/maxwellstefanslaw.hh
index cc9c150481..e62c260163 100644
--- a/dumux/flux/maxwellstefanslaw.hh
+++ b/dumux/flux/maxwellstefanslaw.hh
@@ -17,7 +17,7 @@
* For diffusive mass fluxes \f$\textbf{j}_{diff}^i\f$ the Maxwell-Stefan formulation can be defined as:
*
* \f[
- * \frac{x^i \textbf{grad}_T \eta^i}{RT} = - \sum\limits_{j=1,j\neq i}^{N} \frac{x^ix^j}{D^{ij}}\left(\frac{\textbf{j}_{diff}^i}{\varrho^i}-\frac{\textbf{j}_{diff}^j}{\varrho^j}\right) = -
+ * \frac{x^i \nabla_T \eta^i}{RT} = - \sum\limits_{j=1,j\neq i}^{N} \frac{x^ix^j}{D^{ij}}\left(\frac{\textbf{j}_{diff}^i}{\varrho^i}-\frac{\textbf{j}_{diff}^j}{\varrho^j}\right) = -
* \sum\limits_{j=1,j\neq i}^{N} \frac{x^ix^j}{D^{ij}\varrho}\left(\frac{\textbf{j}_{diff}^i}{X^i}-\frac{\textbf{j}_{diff}^j}{X^j}\right)
* \f]
*
diff --git a/dumux/freeflow/compositional/navierstokesncmodel.hh b/dumux/freeflow/compositional/navierstokesncmodel.hh
index d8ceccb6ba..4c81f0b263 100644
--- a/dumux/freeflow/compositional/navierstokesncmodel.hh
+++ b/dumux/freeflow/compositional/navierstokesncmodel.hh
@@ -16,7 +16,7 @@
* \f[
* \frac{\partial \left(\varrho X^\kappa\right)}{\partial t}
* + \nabla \cdot \left( \varrho {\boldsymbol{v}} X^\kappa
- * - (D^\kappa + D_\text{t}) \varrho \textbf{grad}\, X^\kappa \right)
+ * - (D^\kappa + D_\text{t}) \varrho \nabla X^\kappa \right)
* - q^\kappa = 0
* \f]
*
@@ -25,7 +25,7 @@
* \frac{\partial \varrho_g}{\partial t}
* + \nabla \cdot \left(
* \varrho {\boldsymbol{v}}
- * - \sum_\kappa (D^\kappa + D_\text{t}) \varrho \textbf{grad}\, X^\kappa
+ * - \sum_\kappa (D^\kappa + D_\text{t}) \varrho \nabla X^\kappa
* \right)
* - q = 0
* \f]
diff --git a/dumux/freeflow/navierstokes/energy/model.hh b/dumux/freeflow/navierstokes/energy/model.hh
index cf9161bd5f..ef5e7359af 100644
--- a/dumux/freeflow/navierstokes/energy/model.hh
+++ b/dumux/freeflow/navierstokes/energy/model.hh
@@ -14,7 +14,7 @@
* \f[
* \frac{\partial (\varrho v)}{\partial t}
* + \nabla \cdot \left( \varrho h {\boldsymbol{v}}
- * - \lambda_\text{eff} \textbf{grad}\, T \right) - q_T = 0
+ * - \lambda_\text{eff} \nabla T \right) - q_T = 0
* \f]
*
*
diff --git a/dumux/freeflow/nonisothermal/model.hh b/dumux/freeflow/nonisothermal/model.hh
index 9c6369d06b..53801383f6 100644
--- a/dumux/freeflow/nonisothermal/model.hh
+++ b/dumux/freeflow/nonisothermal/model.hh
@@ -14,7 +14,7 @@
* \f[
* \frac{\partial (\varrho u)}{\partial t}
* + \nabla \cdot \left( \varrho h {\boldsymbol{v}}
- * - \lambda_\text{eff} \textbf{grad}\, T \right) - q_T = 0
+ * - \lambda_\text{eff} \nabla T \right) - q_T = 0
* \f]
*
*
diff --git a/dumux/material/fluidmatrixinteractions/porositydeformation.hh b/dumux/material/fluidmatrixinteractions/porositydeformation.hh
index 8a17093e06..232b7c0228 100644
--- a/dumux/material/fluidmatrixinteractions/porositydeformation.hh
+++ b/dumux/material/fluidmatrixinteractions/porositydeformation.hh
@@ -42,12 +42,12 @@ public:
*
* \note \cite han2003 ( https://doi.org/10.1016/S0920-4105(03)00047-0 )
* provide a derivation for \f$\text{d} \phi = -(1 - \phi ) \text{d} \epsilon_v \f$.
- * Here, \f$\epsilon_v\f$ is equal to \f$\text{div} \mathbf{u}\f$.
+ * Here, \f$\epsilon_v\f$ is equal to \f$\nabla \cdot \mathbf{u}\f$.
* By using an initial porosity \f$\phi_0\f$ and assuming \f$ \epsilon_{v, 0} = 0 \f$,
- * one obtains \f$\phi = \frac{\phi_0 - \text{div} \mathbf{u}}{1 - \text{div} \mathbf{u}}\f$,
+ * one obtains \f$\phi = \frac{\phi_0 - \nabla \cdot \mathbf{u}}{1 - \nabla \cdot \mathbf{u}}\f$,
* which is the formulation for the rock mechanics sign convention. Here we are
* using the continuum mechanics sign convention, thus, the final formula reads:
- * \f$\phi = \frac{\phi_0 + \text{div} \mathbf{u}}{1 + \text{div} \mathbf{u}}\f$.
+ * \f$\phi = \frac{\phi_0 + \nabla \cdot \mathbf{u}}{1 + \nabla \cdot \mathbf{u}}\f$.
*/
template< class FVGridGeom, class ElemSol >
static Scalar evaluatePorosity(const FVGridGeom& gridGeometry,
diff --git a/dumux/material/fluidsystems/3pimmiscible.hh b/dumux/material/fluidsystems/3pimmiscible.hh
index 4f84a38818..e6893298f1 100644
--- a/dumux/material/fluidsystems/3pimmiscible.hh
+++ b/dumux/material/fluidsystems/3pimmiscible.hh
@@ -454,7 +454,7 @@ public:
* Molecular diffusion of a component \f$\mathrm{\kappa}\f$ is caused by a
* gradient of the chemical potential and follows the law
*
- * \f[ J = - D \mathbf{grad} \mu_\kappa \f]
+ * \f[ J = - D \nabla \mu_\kappa \f]
*
* where \f$\mathrm{\mu_\kappa]}\f$ is the component's chemical potential,
* \f$\mathrm{D}\f$ is the diffusion coefficient and \f$\mathrm{J}\f$ is the
diff --git a/dumux/material/fluidsystems/base.hh b/dumux/material/fluidsystems/base.hh
index 5122e25611..a3d276e068 100644
--- a/dumux/material/fluidsystems/base.hh
+++ b/dumux/material/fluidsystems/base.hh
@@ -253,7 +253,7 @@ public:
* Molecular diffusion of a component \f$\mathrm{\kappa}\f$ is caused by a
* gradient of the chemical potential and follows the law
*
- * \f[ J = - D \mathbf{grad} \mu_\kappa \f]
+ * \f[ J = - D \nabla \mu_\kappa \f]
*
* where \f$\mathrm{\mu_\kappa}\f$ is the component's chemical potential,
* \f$\mathrm{D}\f$ is the diffusion coefficient and \f$\mathrm{J}\f$ is the
@@ -283,7 +283,7 @@ public:
* Molecular diffusion of a component \f$\mathrm{\kappa}\f$ is caused by a
* gradient of the chemical potential and follows the law
*
- * \f[ J = - D \mathbf{grad} \mu_\kappa \f]
+ * \f[ J = - D \nabla \mu_\kappa \f]
*
* where \f$\mathrm{\mu_\kappa}\f$ is the component's chemical potential,
* \f$\mathrm{D}\f$ is the diffusion coefficient and \f$\mathrm{J}\f$ is the
diff --git a/dumux/material/fluidsystems/brineco2.hh b/dumux/material/fluidsystems/brineco2.hh
index 06a3a99b75..5d811492ac 100644
--- a/dumux/material/fluidsystems/brineco2.hh
+++ b/dumux/material/fluidsystems/brineco2.hh
@@ -504,7 +504,7 @@ public:
* Molecular diffusion of a component \f$\mathrm{\kappa}\f$ is caused by a
* gradient of the chemical potential and follows the law
*
- * \f[ J = - D \textbf{grad} mu_\kappa \f]
+ * \f[ J = - D \nabla mu_\kappa \f]
*
* where \f$\mathrm{\mu_\kappa}\f$ is the component's chemical potential,
* \f$D\f$ is the diffusion coefficient and \f$\mathrm{J}\f$ is the
diff --git a/dumux/porenetwork/solidenergy/model.hh b/dumux/porenetwork/solidenergy/model.hh
index a278bd2c36..13ada644af 100644
--- a/dumux/porenetwork/solidenergy/model.hh
+++ b/dumux/porenetwork/solidenergy/model.hh
@@ -31,7 +31,7 @@
* The energy balance is described by the following equation:
\f[
\frac{ \partial n c_p \varrho T}{\partial t}
- - \text{div} \left\lbrace \lambda_\text{pm} \textbf{grad} T \right\rbrace = q,
+ - \nabla \cdot \left\lbrace \lambda_\text{pm} \nabla T \right\rbrace = q,
\f]
* where \f$n\f$ is the volume fraction of the conducting material, \f$c_p\f$ its specific heat capacity,
* \f$\varrho\f$ its density, \f$T\f$ the temperature, and \f$\lambda\f$ the heat conductivity of the porous solid.
diff --git a/dumux/porousmediumflow/1p/model.hh b/dumux/porousmediumflow/1p/model.hh
index 974f746043..4d1cc3e273 100644
--- a/dumux/porousmediumflow/1p/model.hh
+++ b/dumux/porousmediumflow/1p/model.hh
@@ -14,8 +14,8 @@
*
* Furthermore, it solves the mass continuity equation
* \f[
- \phi \frac{\partial \varrho}{\partial t} + \text{div} \left\lbrace
- - \varrho \frac{\textbf K}{\mu} \left( \textbf{grad}\, p -\varrho {\textbf g} \right) \right\rbrace = q,
+ \phi \frac{\partial \varrho}{\partial t} + \nabla \cdot \left\lbrace
+ - \varrho \frac{\textbf K}{\mu} \left( \nabla p -\varrho {\textbf g} \right) \right\rbrace = q,
* \f]
* where:
* * \f$ \phi \f$ is the porosity of the porous medium,
diff --git a/dumux/porousmediumflow/1pnc/model.hh b/dumux/porousmediumflow/1pnc/model.hh
index e44629d578..4ebdeb35f1 100644
--- a/dumux/porousmediumflow/1pnc/model.hh
+++ b/dumux/porousmediumflow/1pnc/model.hh
@@ -15,17 +15,17 @@
* Gravity can be enabled or disabled via the property system.
* By inserting Darcy's law into the continuity equation, one gets
\f[
- \phi\frac{\partial \varrho}{\partial t} - \text{div} \left\{
- \varrho \frac{\textbf K}{\mu} \left(\textbf{grad}\, p - \varrho {\textbf g} \right)
+ \phi\frac{\partial \varrho}{\partial t} - \nabla \cdot \left\{
+ \varrho \frac{\textbf K}{\mu} \left(\nabla p - \varrho {\textbf g} \right)
\right\} = q.
\f]
*
* The transport of the components \f$\kappa \in \{ w, a, ... \}\f$ is described by the following equation:
\f[
\phi \frac{ \partial \varrho X^\kappa}{\partial t}
- - \text{div} \left\lbrace \varrho X^\kappa \frac{{\textbf K}}{\mu} \left( \textbf{grad}\, p -
+ - \nabla \cdot \left\lbrace \varrho X^\kappa \frac{{\textbf K}}{\mu} \left( \nabla p -
\varrho {\textbf g} \right)
- + \varrho D^\kappa_\text{pm} \textbf{grad} X^\kappa \right\rbrace = q,
+ + \varrho D^\kappa_\text{pm} \nabla X^\kappa \right\rbrace = q,
\f]
*
* where:
diff --git a/dumux/porousmediumflow/1pncmin/model.hh b/dumux/porousmediumflow/1pncmin/model.hh
index 3c853041f9..5c1bf5a51d 100644
--- a/dumux/porousmediumflow/1pncmin/model.hh
+++ b/dumux/porousmediumflow/1pncmin/model.hh
@@ -19,10 +19,10 @@
* components, one gets one transport equation for each component,
* \f[
\frac{\partial ( \varrho_f X^\kappa \phi )}
-{\partial t} - \text{div} \left\{ \varrho_f X^\kappa
+{\partial t} - \nabla \cdot \left\{ \varrho_f X^\kappa
\frac{k_{r}}{\mu} \mathbf{K}
-(\text{grad}\, p - \varrho_{f} \mathbf{g}) \right\}
-- \text{div} \left\{{\bf D_{pm}^\kappa} \varrho_{f} \text{grad}\, X^\kappa \right\}
+(\nabla p - \varrho_{f} \mathbf{g}) \right\}
+- \nabla \cdot \left\{{\bf D_{pm}^\kappa} \varrho_{f} \nabla X^\kappa \right\}
- q_\kappa = 0 \qquad \kappa \in \{w, a,\cdots \},
* \f]
* where:
diff --git a/dumux/porousmediumflow/2p/model.hh b/dumux/porousmediumflow/2p/model.hh
index ea762c5ec9..fe7adb6fbe 100644
--- a/dumux/porousmediumflow/2p/model.hh
+++ b/dumux/porousmediumflow/2p/model.hh
@@ -19,8 +19,8 @@
\f[
\phi \frac{\partial \varrho_\alpha S_\alpha}{\partial t}
-
- \text{div} \left\{
- \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right)
+ \nabla \cdot \left\{
+ \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\nabla p_\alpha - \varrho_{\alpha} \mathbf{g} \right)
\right\} - q_\alpha = 0,
\f]
*where:
diff --git a/dumux/porousmediumflow/2p1c/model.hh b/dumux/porousmediumflow/2p1c/model.hh
index aadf24482a..a34e4799f0 100644
--- a/dumux/porousmediumflow/2p1c/model.hh
+++ b/dumux/porousmediumflow/2p1c/model.hh
@@ -23,8 +23,8 @@
* By inserting Darcy's law into the equations for the conservation of the
* phase mass, one gets
\f[
-\phi \frac{\partial\ \sum_\alpha (\rho_\alpha S_\alpha)}{\partial t} \\-\sum \limits_ \alpha \text{div} \left \{\rho_\alpha \frac{k_{r\alpha}}{\mu_\alpha}
-\mathbf{K} (\mathbf{grad}p_\alpha - \rho_\alpha \mathbf{g}) \right \} -q^w =0,
+\phi \frac{\partial\ \sum_\alpha (\rho_\alpha S_\alpha)}{\partial t} \\-\sum \limits_ \alpha \nabla \cdot \left \{\rho_\alpha \frac{k_{r\alpha}}{\mu_\alpha}
+\mathbf{K} (\nabla p_\alpha - \rho_\alpha \mathbf{g}) \right \} -q^w =0,
\f]
* where:
* * \f$ \phi \f$ is the porosity of the porous medium,
diff --git a/dumux/porousmediumflow/2p2c/model.hh b/dumux/porousmediumflow/2p2c/model.hh
index 4b388d2ccb..e50ef401f2 100644
--- a/dumux/porousmediumflow/2p2c/model.hh
+++ b/dumux/porousmediumflow/2p2c/model.hh
@@ -17,15 +17,15 @@
* depending on the property <tt>UseMoles</tt>. The mass balance equations are given as
* \f[
\phi \frac{\partial (\sum_\alpha \rho_\alpha X_\alpha^\kappa S_\alpha)}{\partial t}
- - \sum_\alpha \text{div} \left\{ \rho_\alpha X_\alpha^\kappa v_\alpha \right\}
- - \sum_\alpha \text{div} \mathbf{F}_{\mathrm{diff, mass}, \alpha}^\kappa
+ - \sum_\alpha \nabla \cdot \left\{ \rho_\alpha X_\alpha^\kappa v_\alpha \right\}
+ - \sum_\alpha \nabla \cdot \mathbf{F}_{\mathrm{diff, mass}, \alpha}^\kappa
- \sum_\alpha q_\alpha^\kappa = 0 \qquad \kappa \in \{\kappa_w, \kappa_n\} \, , \alpha \in \{w, n\}.
\f]
* The mole balance is given as
* \f[
\phi \frac{\partial (\sum_\alpha \varrho_{m, \alpha} x_\alpha^\kappa S_\alpha)}{\partial t}
- + \sum_\alpha \text{div} \left\{ \varrho_{m, \alpha} x_\alpha^\kappa v_\alpha \right\}
- + \sum_\alpha \text{div} \mathbf{F}_{\mathrm{diff, mole}, \alpha}^\kappa
+ + \sum_\alpha \nabla \cdot \left\{ \varrho_{m, \alpha} x_\alpha^\kappa v_\alpha \right\}
+ + \sum_\alpha \nabla \cdot \mathbf{F}_{\mathrm{diff, mole}, \alpha}^\kappa
- \sum_\alpha q_\alpha^\kappa = 0 \qquad \kappa \in \{\kappa_w, \kappa_n\} \, , \alpha \in \{w, n\},
\f]
* where:
diff --git a/dumux/porousmediumflow/2pnc/model.hh b/dumux/porousmediumflow/2pnc/model.hh
index c4eeee6390..85d42a3c10 100644
--- a/dumux/porousmediumflow/2pnc/model.hh
+++ b/dumux/porousmediumflow/2pnc/model.hh
@@ -22,11 +22,11 @@
* \f{eqnarray*}{
* && \frac{\partial (\sum_\alpha \varrho_\alpha X_\alpha^\kappa \phi S_\alpha )}
* {\partial t}
- * - \sum_\alpha \text{div} \left\{ \varrho_\alpha X_\alpha^\kappa
+ * - \sum_\alpha \nabla \cdot \left\{ \varrho_\alpha X_\alpha^\kappa
* \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K}
- * (\text{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g}) \right\}
+ * (\nabla p_\alpha - \varrho_{\alpha} \mathbf{g}) \right\}
* \nonumber \\ \nonumber \\
- * &-& \sum_\alpha \text{div} \left\{{\bf D_{\alpha, pm}^\kappa} \varrho_{\alpha} \text{grad}\, X^\kappa_{\alpha} \right\}
+ * &-& \sum_\alpha \nabla \cdot \left\{{\bf D_{\alpha, pm}^\kappa} \varrho_{\alpha} \nabla X^\kappa_{\alpha} \right\}
* - \sum_\alpha q_\alpha^\kappa = 0 \qquad \kappa \in \{w, a,\cdots \} \, ,
* \alpha \in \{w, g\},
* \f}
diff --git a/dumux/porousmediumflow/2pncmin/model.hh b/dumux/porousmediumflow/2pncmin/model.hh
index ed403351ba..a10644a7cd 100644
--- a/dumux/porousmediumflow/2pncmin/model.hh
+++ b/dumux/porousmediumflow/2pncmin/model.hh
@@ -22,11 +22,11 @@
* \f{eqnarray*}{
* && \frac{\partial (\sum_\alpha \varrho_\alpha X_\alpha^\kappa \phi S_\alpha )}
* {\partial t}
- * - \sum_\alpha \text{div} \left\{ \varrho_\alpha X_\alpha^\kappa
+ * - \sum_\alpha \nabla \cdot \left\{ \varrho_\alpha X_\alpha^\kappa
* \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K}
- * (\text{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g}) \right\}
+ * (\nabla p_\alpha - \varrho_{\alpha} \mathbf{g}) \right\}
* \nonumber \\ \nonumber \\
- * &-& \sum_\alpha \text{div} \left\{{\bf D_{\alpha, pm}^\kappa} \varrho_{\alpha} \text{grad}\, X^\kappa_{\alpha} \right\}
+ * &-& \sum_\alpha \nabla \cdot \left\{{\bf D_{\alpha, pm}^\kappa} \varrho_{\alpha} \nabla X^\kappa_{\alpha} \right\}
* - \sum_\alpha q_\alpha^\kappa = 0 \qquad \kappa \in \{w, a,\cdots \} \, ,
* \alpha \in \{w, g\},
* \f}
diff --git a/dumux/porousmediumflow/3p/model.hh b/dumux/porousmediumflow/3p/model.hh
index 93355b96a1..d2fc6cd27a 100644
--- a/dumux/porousmediumflow/3p/model.hh
+++ b/dumux/porousmediumflow/3p/model.hh
@@ -20,8 +20,8 @@
\f[
\phi \frac{\partial \varrho_\alpha S_\alpha}{\partial t}
-
- \text{div} \left\{
- \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right)
+ \nabla \cdot \left\{
+ \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\nabla p_\alpha - \varrho_{\alpha} \mathbf{g} \right)
\right\} - q_\alpha = 0,
\f]
* where:
diff --git a/dumux/porousmediumflow/3p3c/model.hh b/dumux/porousmediumflow/3p3c/model.hh
index 4896a2b9ba..b41ba06e32 100644
--- a/dumux/porousmediumflow/3p3c/model.hh
+++ b/dumux/porousmediumflow/3p3c/model.hh
@@ -21,13 +21,13 @@
* \f{eqnarray*}
&& \phi \frac{\partial (\sum_\alpha \varrho_{\alpha,mol} x_\alpha^\kappa
S_\alpha )}{\partial t}
- - \sum\limits_\alpha \text{div} \left\{ \frac{k_{r\alpha}}{\mu_\alpha}
+ - \sum\limits_\alpha \nabla \cdot \left\{ \frac{k_{r\alpha}}{\mu_\alpha}
\varrho_{\alpha,mol} x_\alpha^\kappa \mathbf{K}
- (\textbf{grad}\, p_\alpha - \varrho_{\alpha,mass} \mathbf{g}) \right\}
+ (\nabla p_\alpha - \varrho_{\alpha,mass} \mathbf{g}) \right\}
\nonumber \\
\nonumber \\
- && - \sum\limits_\alpha \text{div} \left\{ D_\text{pm}^\kappa \frac{1}{M_{\kappa}} \varrho_{\alpha}
- \textbf{grad} X^\kappa_{\alpha} \right\}
+ && - \sum\limits_\alpha \nabla \cdot \left\{ D_\text{pm}^\kappa \frac{1}{M_{\kappa}} \varrho_{\alpha}
+ \nabla X^\kappa_{\alpha} \right\}
- q^\kappa = 0 \qquad \forall \kappa , \; \forall \alpha,
\f}
* where:
diff --git a/dumux/porousmediumflow/3pwateroil/model.hh b/dumux/porousmediumflow/3pwateroil/model.hh
index 3a167f89f3..02806c10bd 100644
--- a/dumux/porousmediumflow/3pwateroil/model.hh
+++ b/dumux/porousmediumflow/3pwateroil/model.hh
@@ -22,13 +22,13 @@
* \f{eqnarray*}
&& \phi \frac{\partial (\sum_\alpha \varrho_\alpha X_\alpha^\kappa
S_\alpha )}{\partial t}
- - \sum\limits_\alpha \text{div} \left\{ \frac{k_{r\alpha}}{\mu_\alpha}
+ - \sum\limits_\alpha \nabla \cdot \left\{ \frac{k_{r\alpha}}{\mu_\alpha}
\varrho_\alpha x_\alpha^\kappa \mathbf{K}
- (\textbf{grad}\, p_\alpha - \varrho_\alpha \mathbf{g}) \right\}
+ (\nabla p_\alpha - \varrho_\alpha \mathbf{g}) \right\}
\nonumber \\
\nonumber \\
- && - \sum\limits_\alpha \text{div} \left\{ D_\text{pm}^\kappa \varrho_\alpha \frac{1}{M_\kappa}
- \textbf{grad} X^\kappa_{\alpha} \right\}
+ && - \sum\limits_\alpha \nabla \cdot \left\{ D_\text{pm}^\kappa \varrho_\alpha \frac{1}{M_\kappa}
+ \nabla X^\kappa_{\alpha} \right\}
- q^\kappa = 0 \qquad \forall \kappa , \; \forall \alpha,
\f}
*
diff --git a/dumux/porousmediumflow/nonisothermal/model.hh b/dumux/porousmediumflow/nonisothermal/model.hh
index 7d4593ac2b..024e76c4d1 100644
--- a/dumux/porousmediumflow/nonisothermal/model.hh
+++ b/dumux/porousmediumflow/nonisothermal/model.hh
@@ -23,13 +23,13 @@
& +
\left( 1 - \phi \right) \frac{\partial (\varrho_s c_s T)}{\partial t}
-
- \sum_\alpha \text{div}
+ \sum_\alpha \nabla \cdot
\left\{
\varrho_\alpha h_\alpha
\frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K}
- \left( \textbf{grad}\,p_\alpha - \varrho_\alpha \mathbf{g} \right)
+ \left( \nabla p_\alpha - \varrho_\alpha \mathbf{g} \right)
\right\} \\
- & - \text{div} \left(\lambda_{pm} \textbf{grad} \, T \right)
+ & - \nabla \cdot \left(\lambda_{pm} \nabla T \right)
- q^h = 0,
\f}
* where:
diff --git a/dumux/porousmediumflow/richards/model.hh b/dumux/porousmediumflow/richards/model.hh
index e1f00351fa..01efffdcb7 100644
--- a/dumux/porousmediumflow/richards/model.hh
+++ b/dumux/porousmediumflow/richards/model.hh
@@ -14,9 +14,9 @@
\f[
\frac{\partial\;\phi S_w \varrho_w}{\partial t}
-
- \text{div} \left\lbrace
+ \nabla \cdot \left\lbrace
\varrho_w \frac{k_{rw}}{\mu_w} \; \mathbf{K} \;
- \left( \textbf{grad}
+ \left( \nabla
p_w - \varrho_w \textbf{g}
\right)
\right\rbrace
@@ -31,9 +31,9 @@
\f[
\phi\frac{\partial S_\alpha \varrho_\alpha}{\partial t}
-
- \text{div} \left\lbrace
+ \nabla \cdot \left\lbrace
\varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha}\; \mathbf{K} \;
- \left(\textbf{grad}
+ \left(\nabla
p_\alpha - \varrho_\alpha \textbf{g}
\right)
\right\rbrace
diff --git a/dumux/porousmediumflow/richardsextended/model.hh b/dumux/porousmediumflow/richardsextended/model.hh
index 4d76a3039a..f3e0749cf6 100644
--- a/dumux/porousmediumflow/richardsextended/model.hh
+++ b/dumux/porousmediumflow/richardsextended/model.hh
@@ -16,13 +16,13 @@
+
\frac{\partial\;\phi (1-S_w)\varrho_n X_n^w}{\partial t}
-
- \text{div} \left\lbrace
+ \nabla \cdot \left\lbrace
\varrho_w \frac{k_{rw}}{\mu_w} \; \mathbf{K} \;
- \left( \text{\textbf{grad}}
+ \left( \text{\nabla}
p_w - \varrho_w \textbf{g}
\right)
+
- {\bf D_{n, pm}^w} \varrho_n \text{grad}\, X^w_n
+ {\bf D_{n, pm}^w} \varrho_n \nabla X^w_n
\right\rbrace
=
q_w,
@@ -48,9 +48,9 @@
\f[
\phi\frac{\partial S_\alpha \varrho_\alpha}{\partial t}
-
- \text{div} \left\lbrace
+ \nabla \cdot \left\lbrace
\varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha}\; \mathbf{K} \;
- \left( \text{\textbf{grad}}
+ \left( \text{\nabla}
p_\alpha - \varrho_\alpha \textbf{g}
\right)
\right\rbrace
diff --git a/dumux/porousmediumflow/richardsnc/model.hh b/dumux/porousmediumflow/richardsnc/model.hh
index b676878463..737f318cd6 100644
--- a/dumux/porousmediumflow/richardsnc/model.hh
+++ b/dumux/porousmediumflow/richardsnc/model.hh
@@ -14,11 +14,11 @@
*\f{eqnarray*}
&& \frac{\partial (\sum_w \varrho_w X_w^\kappa \phi S_w )}
{\partial t}
- - \sum_w \text{div} \left\{ \varrho_w X_w^\kappa
+ - \sum_w \nabla \cdot \left\{ \varrho_w X_w^\kappa
\frac{k_{rw}}{\mu_w} \mathbf{K}
- (\text{grad}\, p_w - \varrho_{w} \mathbf{g}) \right\}
+ (\nabla p_w - \varrho_{w} \mathbf{g}) \right\}
\nonumber \\ \nonumber \\
- &-& \sum_w \text{div} \left\{{\bf D_{w, pm}^\kappa} \varrho_{w} \text{grad}\, X^\kappa_{w} \right\}
+ &-& \sum_w \nabla \cdot \left\{{\bf D_{w, pm}^\kappa} \varrho_{w} \nabla X^\kappa_{w} \right\}
- \sum_w q_w^\kappa = 0 \qquad \kappa \in \{w, a,\cdots \} \, ,
w \in \{w, g\},
\f}
diff --git a/dumux/porousmediumflow/solidenergy/model.hh b/dumux/porousmediumflow/solidenergy/model.hh
index 0ab5964836..cffb23ec70 100644
--- a/dumux/porousmediumflow/solidenergy/model.hh
+++ b/dumux/porousmediumflow/solidenergy/model.hh
@@ -13,7 +13,7 @@
* The energy balance is described by the following equation:
\f[
\frac{ \partial n c_p \varrho T}{\partial t}
- - \text{div} \left\lbrace \lambda_\text{pm} \textbf{grad} T \right\rbrace = q,
+ - \nabla \cdot \left\lbrace \lambda_\text{pm} \nabla T \right\rbrace = q,
\f]
* where:
* * \f$ n \f$ represents volume fraction of the conducting material,
diff --git a/dumux/porousmediumflow/tracer/model.hh b/dumux/porousmediumflow/tracer/model.hh
index c9b4242c29..4c4efa24f1 100644
--- a/dumux/porousmediumflow/tracer/model.hh
+++ b/dumux/porousmediumflow/tracer/model.hh
@@ -20,8 +20,8 @@
* The transport of the components \f$\kappa \in \{ a, b, c, ... \}\f$ is described by the following equation:
\f[
\phi \frac{ \partial \varrho X^\kappa}{\partial t}
- - \text{div} \left\lbrace \varrho X^\kappa {\textbf v_f}
- + \varrho D^\kappa_\text{pm} \textbf{grad} X^\kappa \right\rbrace = q,
+ - \nabla \cdot \left\lbrace \varrho X^\kappa {\textbf v_f}
+ + \varrho D^\kappa_\text{pm} \nabla X^\kappa \right\rbrace = q,
\f]
* where:
* * \f$ \phi \f$ is the porosity of the porous medium,
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