From f6e09ecf66bed9344fa7506c3bb909abbbd02995 Mon Sep 17 00:00:00 2001
From: Kilian Weishaupt <kilian.weishaupt@iws.uni-stuttgart.de>
Date: Mon, 7 Sep 2020 08:06:09 +0200
Subject: [PATCH] [navierstokes][localresidual] Add source term for
axisymmetric problems
---
.../navierstokes/staggered/localresidual.hh | 18 ++++++++++++++++++
1 file changed, 18 insertions(+)
diff --git a/dumux/freeflow/navierstokes/staggered/localresidual.hh b/dumux/freeflow/navierstokes/staggered/localresidual.hh
index 64083aa458..6baa841272 100644
--- a/dumux/freeflow/navierstokes/staggered/localresidual.hh
+++ b/dumux/freeflow/navierstokes/staggered/localresidual.hh
@@ -169,6 +169,24 @@ public:
source += problem.gravity()[scvf.directionIndex()] * insideVolVars.density();
source += problem.source(element, fvGeometry, elemVolVars, elemFaceVars, scvf)[Indices::velocity(scvf.directionIndex())];
+ // Axisymmetric problems in 2D feature an extra source terms arising from the transformation to cylindrical coordinates.
+ // See Ferziger/Peric: Computational methods for fluid dynamics chapter 8.
+ // https://doi.org/10.1007/978-3-540-68228-8 (page 301)
+ if constexpr (ModelTraits::dim() == 2 && std::is_same_v<Extrusion, RotationalExtrusion<Extrusion::radialAxis>>)
+ {
+ if (scvf.directionIndex() == Extrusion::radialAxis)
+ {
+ // Velocity term
+ const auto r = scvf.center()[scvf.directionIndex()];
+ source -= -2.0*insideVolVars.effectiveViscosity() * elemFaceVars[scvf].velocitySelf() / (r*r);
+
+ // Pressure term (needed because we incorporate pressure in terms of a surface integral).
+ // grad(p) becomes div(pI) + (p/r)*n_r in cylindrical coordinates. The second term
+ // is new with respect to Cartesian coordinates and handled below as a source term.
+ source += insideVolVars.pressure()/r;
+ }
+ }
+
return source;
}
--
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