From c9b4993730bc93cabdaf0e9eb18dc9dee5cac3c9 Mon Sep 17 00:00:00 2001
From: Kilian Weishaupt <kilian.weishaupt@iws.uni-stuttgart.de>
Date: Tue, 24 Apr 2018 08:25:55 +0200
Subject: [PATCH] [navierstokes] Add convenience function to calculate pseudo
3D friction term
---
doc/handbook/dumux-handbook.bib | 28 +++++++++++++++-
dumux/freeflow/navierstokes/problem.hh | 44 ++++++++++++++++++++++++--
2 files changed, 68 insertions(+), 4 deletions(-)
diff --git a/doc/handbook/dumux-handbook.bib b/doc/handbook/dumux-handbook.bib
index 2f050249d5..6264fca6b7 100644
--- a/doc/handbook/dumux-handbook.bib
+++ b/doc/handbook/dumux-handbook.bib
@@ -1068,7 +1068,7 @@ url = {http://www.sciencedirect.com/science/article/pii/S0169772204001160}
volume = {198},
pages = {71--78}
}
-@misc{cooper2008,
+@misc{cooper2008,
title={{Release of the IAPWS formulation 2008 for the viscosity of ordinary water substance}},
author={Cooper, J. R. and Dooley, R. B.},
year={2008},
@@ -1676,3 +1676,29 @@ url={http://dx.doi.org/10.1007/s11242-015-0599-1}
doi = {10.1115/1.3240815},
url = {http://dx.doi.org/10.1115/1.3240815},
}
+
+@Article{flekkoy1995a,
+ title={{Hydrodynamic dispersion at stagnation points: Simulations and experiments}},
+ author={{Flekk{\o}y, EG and Oxaal, U and Feder, J and J{\o}ssang, T}},
+ journal={Physical Review E},
+ volume={52},
+ number={5},
+ pages={4952},
+ year={1995},
+ publisher={APS},
+ doi = {10.1103/PhysRevE.52.4952},
+ url = {https://doi.org/10.1103/PhysRevE.52.4952}
+}
+
+@Article{venturoli2006a,
+ title={{Two-dimensional lattice-Boltzmann simulations of single phase flow in a pseudo two-dimensional micromodel}},
+ author={{Venturoli, Maddalena and Boek, Edo S}},
+ journal={Physica A: Statistical Mechanics and its Applications},
+ volume={362},
+ number={1},
+ pages={23--29},
+ year={2006},
+ publisher={Elsevier},
+ doi = {10.1016/j.physa.2005.09.006},
+ url = {https://doi.org/10.1016/j.physa.2005.09.006}
+ }
diff --git a/dumux/freeflow/navierstokes/problem.hh b/dumux/freeflow/navierstokes/problem.hh
index 376b5d843f..58d178085d 100644
--- a/dumux/freeflow/navierstokes/problem.hh
+++ b/dumux/freeflow/navierstokes/problem.hh
@@ -116,19 +116,57 @@ public:
* If the <tt>Problem.EnableGravity</tt> parameter is true, this means
* \f$\boldsymbol{g} = ( 0,\dots,\ -9.81)^T \f$, else \f$\boldsymbol{g} = ( 0,\dots, 0)^T \f$
*/
- const GlobalPosition &gravity() const
+ const GlobalPosition& gravity() const
{ return gravity_; }
//! Applys the initial face solution (velocities on the faces). Specialization for staggered grid discretization.
template <class G = FVGridGeometry>
typename std::enable_if<G::discMethod == DiscretizationMethod::staggered, void>::type
applyInitialFaceSolution(SolutionVector& sol,
- const SubControlVolumeFace& scvf,
- const PrimaryVariables& initSol) const
+ const SubControlVolumeFace& scvf,
+ const PrimaryVariables& initSol) const
{
sol[FVGridGeometry::faceIdx()][scvf.dofIndex()][0] = initSol[Indices::velocity(scvf.directionIndex())];
}
+
+ /*!
+ * \brief An additional drag term can be included as source term for the momentum balance
+ * to mimic 3D flow behavior in 2D:
+ * \f[
+ * f_{drag} = -(8 \mu / h^2)v
+ * \f]
+ * Here, \f$h\f$ corresponds to the extruded height that is
+ * bounded by the imaginary walls. See Flekkoy et al. (1995) \cite flekkoy1995a<BR>
+ * A value of 8.0 is used as a default factor, corresponding
+ * to the velocity profile at the center plane
+ * of the virtual height (maximum velocity). Setting this value to 12.0 corresponds
+ * to an depth-averaged velocity (Venturoli and Boek, 2006) \cite venturoli2006a.
+ */
+ Scalar pseudo3DWallFriction(const Scalar velocity,
+ const Scalar viscosity,
+ const Scalar height,
+ const Scalar factor = 8.0) const
+ {
+ static_assert(dim == 2, "Pseudo 3D wall friction may only be used in 2D");
+ return -factor * velocity * viscosity / (height*height);
+ }
+
+ //! Convenience function for staggered grid implementation.
+ template <class ElementVolumeVariables, class ElementFaceVariables, class G = FVGridGeometry>
+ typename std::enable_if<G::discMethod == DiscretizationMethod::staggered, Scalar>::type
+ pseudo3DWallFriction(const SubControlVolumeFace& scvf,
+ const ElementVolumeVariables& elemVolVars,
+ const ElementFaceVariables& elemFaceVars,
+ const Scalar height,
+ const Scalar factor = 8.0) const
+ {
+ const Scalar velocity = elemFaceVars[scvf].velocitySelf();
+ const Scalar viscosity = elemVolVars[scvf.insideScvIdx()].effectiveViscosity();
+ return pseudo3DWallFriction(velocity, viscosity, height, factor);
+ }
+
+
private:
//! Returns the implementation of the problem (i.e. static polymorphism)
--
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