diff --git a/dumux/freeflow/navierstokes/staggered/staggeredupwindfluxvariables.hh b/dumux/freeflow/navierstokes/staggered/staggeredupwindfluxvariables.hh
index 544eeac6c4cad4a9681bc9abae0d23b650428993..9d0767d2a1604972092cc74ba1ef3398faecc253 100644
--- a/dumux/freeflow/navierstokes/staggered/staggeredupwindfluxvariables.hh
+++ b/dumux/freeflow/navierstokes/staggered/staggeredupwindfluxvariables.hh
@@ -72,9 +72,6 @@ class StaggeredUpwindFluxVariables
using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
static constexpr bool useHigherOrder = upwindSchemeOrder > 1;
- static constexpr auto cellCenterIdx = FVGridGeometry::cellCenterIdx();
- static constexpr auto faceIdx = FVGridGeometry::faceIdx();
-
public:
/*!
* \brief Returns the momentum in the frontal directon.
@@ -90,23 +87,20 @@ public:
const GridFluxVariablesCache& gridFluxVarsCache,
const Scalar transportingVelocity)
{
- Scalar momentum(0.0);
const bool canHigherOrder = canFrontalSecondOrder_(scvf, transportingVelocity, std::integral_constant<bool, useHigherOrder>{});
if (canHigherOrder)
{
const auto upwindingMomenta = getFrontalUpwindingMomenta_(scvf, elemFaceVars, elemVolVars[scvf.insideScvIdx()].density(),
transportingVelocity, std::integral_constant<bool, useHigherOrder>{});
- momentum = doFrontalMomentumUpwinding_(scvf, upwindingMomenta, transportingVelocity, gridFluxVarsCache);
+ return doFrontalMomentumUpwinding_(scvf, upwindingMomenta, transportingVelocity, gridFluxVarsCache);
}
else
{
const auto upwindingMomenta = getFrontalUpwindingMomenta_(scvf, elemFaceVars, elemVolVars[scvf.insideScvIdx()].density(),
transportingVelocity, std::integral_constant<bool, false>{});
- momentum = doFrontalMomentumUpwinding_(scvf, upwindingMomenta, transportingVelocity, gridFluxVarsCache);
+ return doFrontalMomentumUpwinding_(scvf, upwindingMomenta, transportingVelocity, gridFluxVarsCache);
}
-
- return momentum;
}
/*!
@@ -137,7 +131,6 @@ public:
// Check whether the own or the neighboring element is upstream.
const bool selfIsUpstream = ( normalFace.directionSign() == sign(transportingVelocity) );
- Scalar momentum(0.0);
const bool canHigherOrder = canLateralSecondOrder_(scvf, selfIsUpstream, localSubFaceIdx, std::integral_constant<bool, useHigherOrder>{});
if (canHigherOrder)
@@ -146,7 +139,7 @@ public:
transportingVelocity, localSubFaceIdx,
lateralFaceHasDirichletPressure, lateralFaceHasBJS,
std::integral_constant<bool, useHigherOrder>{});
- momentum = doLateralMomentumUpwinding_(scvf, normalFace, parallelUpwindingMomenta, transportingVelocity, localSubFaceIdx, gridFluxVarsCache);
+ return doLateralMomentumUpwinding_(scvf, normalFace, parallelUpwindingMomenta, transportingVelocity, localSubFaceIdx, gridFluxVarsCache);
}
else
{
@@ -154,10 +147,8 @@ public:
transportingVelocity, localSubFaceIdx,
lateralFaceHasDirichletPressure, lateralFaceHasBJS,
std::integral_constant<bool, false>{});
- momentum = doLateralMomentumUpwinding_(scvf, normalFace, parallelUpwindingMomenta, transportingVelocity, localSubFaceIdx, gridFluxVarsCache);
+ return doLateralMomentumUpwinding_(scvf, normalFace, parallelUpwindingMomenta, transportingVelocity, localSubFaceIdx, gridFluxVarsCache);
}
-
- return momentum;
}
private:
@@ -174,9 +165,7 @@ private:
static bool canFrontalSecondOrder_(const SubControlVolumeFace& ownScvf,
const Scalar transportingVelocity,
std::false_type)
- {
- return false;
- }
+ { return false; }
/*!
* \brief Returns whether or not the face in question is far enough from the wall to handle higher order methods.
@@ -199,19 +188,9 @@ private:
const bool selfIsUpstream = ownScvf.directionSign() != sign(transportingVelocity);
if (selfIsUpstream)
- {
- if (ownScvf.hasForwardNeighbor(0))
- return true;
- else
- return false;
- }
+ return ownScvf.hasForwardNeighbor(0);
else
- {
- if (ownScvf.hasBackwardNeighbor(0))
- return true;
- else
- return false;
- }
+ return ownScvf.hasBackwardNeighbor(0);
}
/*!
@@ -253,7 +232,7 @@ private:
std::true_type)
{
const bool selfIsUpstream = scvf.directionSign() != sign(transportingVelocity);
- std::array<Scalar, 3> momenta{0.0, 0.0, 0.0};
+ std::array<Scalar, 3> momenta;
if (selfIsUpstream)
{
@@ -320,7 +299,7 @@ private:
{
// Depending on selfIsUpstream the downstream and the (up)upstream distances are saved.
// distances {upstream to downstream distance, up-upstream to upstream distance, downstream staggered cell size}
- std::array<Scalar, 3> distances{0.0, 0.0, 0.0};
+ std::array<Scalar, 3> distances;
if (selfIsUpstream)
{
@@ -362,10 +341,7 @@ private:
else
{
// The self velocity is downstream. If there is no parallel neighbor I cannot use a second order approximation.
- if (!ownScvf.hasParallelNeighbor(localSubFaceIdx, 0))
- return false;
- else
- return true;
+ return ownScvf.hasParallelNeighbor(localSubFaceIdx, 0);
}
}
@@ -397,24 +373,34 @@ private:
bool lateralFaceHasBJS,
std::true_type)
{
- std::array<Scalar, 3> momenta{0.0, 0.0, 0.0};
const SubControlVolumeFace& lateralFace = fvGeometry.scvf(ownScvf.insideScvIdx(), ownScvf.pairData(localSubFaceIdx).localNormalFaceIdx);
- // Check whether the own or the neighboring element is upstream.
- const bool selfIsUpstream = lateralFace.directionSign() == sign(transportingVelocity);
-
// Get the volume variables of the own and the neighboring element
const auto& insideVolVars = elemVolVars[lateralFace.insideScvIdx()];
const auto& outsideVolVars = elemVolVars[lateralFace.outsideScvIdx()];
- // The local index of the faces that is opposite to localSubFaceIdx
- const int oppositeSubFaceIdx = localSubFaceIdx % 2 ? localSubFaceIdx - 1 : localSubFaceIdx + 1;
+ // If the lateral face lies on a boundary, we assume that the parallel velocity on the boundary is actually known,
+ // thus we always use this value for the computation of the transported momentum.
+ if (!ownScvf.hasParallelNeighbor(localSubFaceIdx, 0))
+ {
+ const Scalar boundaryMomentum = getParallelVelocityFromBoundary_(problem, ownScvf, lateralFace,
+ faceVars.velocitySelf(), localSubFaceIdx,
+ element, lateralFaceHasDirichletPressure,
+ lateralFaceHasBJS) * insideVolVars.density();
+
+ return std::array<Scalar, 3>{boundaryMomentum, boundaryMomentum, boundaryMomentum};
+ }
+
+ // Check whether the own or the neighboring element is upstream.
+ const bool selfIsUpstream = lateralFace.directionSign() == sign(transportingVelocity);
+
+ std::array<Scalar, 3> momenta;
if (selfIsUpstream)
{
momenta[1] = faceVars.velocitySelf() * insideVolVars.density();
- if(ownScvf.hasParallelNeighbor(localSubFaceIdx, 0))
+ if (ownScvf.hasParallelNeighbor(localSubFaceIdx, 0))
momenta[0] = faceVars.velocityParallel(localSubFaceIdx, 0) * insideVolVars.density();
else
momenta[0] = getParallelVelocityFromBoundary_(problem, ownScvf, lateralFace,
@@ -422,6 +408,9 @@ private:
element, lateralFaceHasDirichletPressure,
lateralFaceHasBJS) * insideVolVars.density();
+ // The local index of the faces that is opposite to localSubFaceIdx
+ const int oppositeSubFaceIdx = localSubFaceIdx % 2 ? localSubFaceIdx - 1 : localSubFaceIdx + 1;
+
// The "upstream-upstream" velocity is retrieved from the other parallel neighbor or from the boundary.
if (ownScvf.hasParallelNeighbor(oppositeSubFaceIdx, 0))
momenta[2] = faceVars.velocityParallel(oppositeSubFaceIdx, 0) * insideVolVars.density();
@@ -447,8 +436,8 @@ private:
(momenta[1]/outsideVolVars.density())) * outsideVolVars.density();
}
}
- return momenta;
+ return momenta;
}
/*!
@@ -470,14 +459,11 @@ private:
{
// Check whether the own or the neighboring element is upstream.
const SubControlVolumeFace& lateralFace = fvGeometry.scvf(ownScvf.insideScvIdx(), ownScvf.pairData(localSubFaceIdx).localNormalFaceIdx);
- const bool selfIsUpstream = lateralFace.directionSign() == sign(transportingVelocity);
// Get the volume variables of the own and the neighboring element
const auto& insideVolVars = elemVolVars[lateralFace.insideScvIdx()];
const auto& outsideVolVars = elemVolVars[lateralFace.outsideScvIdx()];
- const Scalar momentumSelf = faceVars.velocitySelf() * insideVolVars.density();
-
const Scalar momentumParallel = ownScvf.hasParallelNeighbor(localSubFaceIdx, 0)
? faceVars.velocityParallel(localSubFaceIdx, 0) * outsideVolVars.density()
: (getParallelVelocityFromBoundary_(problem, ownScvf, lateralFace,
@@ -485,6 +471,14 @@ private:
lateralFaceHasDirichletPressure, lateralFaceHasBJS)
* insideVolVars.density());
+ // If the lateral face lies on a boundary, we assume that the parallel velocity on the boundary is actually known,
+ // thus we always use this value for the computation of the transported momentum.
+ if (!ownScvf.hasParallelNeighbor(localSubFaceIdx, 0))
+ return std::array<Scalar, 2>{momentumParallel, momentumParallel};
+
+ const bool selfIsUpstream = lateralFace.directionSign() == sign(transportingVelocity);
+ const Scalar momentumSelf = faceVars.velocitySelf() * insideVolVars.density();
+
return selfIsUpstream ? std::array<Scalar, 2>{momentumParallel, momentumSelf}
: std::array<Scalar, 2>{momentumSelf, momentumParallel};
}
@@ -540,16 +534,16 @@ private:
const bool selfIsUpstream)
{
// distances {upstream to downstream distance, up-upstream to upstream distance, downstream staggered cell size}
- std::array<Scalar, 3> distances{0.0, 0.0, 0.0};
-
- // The local index of the faces that is opposite to localSubFaceIdx
- const int oppositeSubFaceIdx = localSubFaceIdx % 2 ? localSubFaceIdx - 1 : localSubFaceIdx + 1;
+ std::array<Scalar, 3> distances;
if (selfIsUpstream)
{
+ // The local index of the faces that is opposite to localSubFaceIdx
+ const int oppositeSubFaceIdx = localSubFaceIdx % 2 ? localSubFaceIdx - 1 : localSubFaceIdx + 1;
+
distances[0] = ownScvf.cellCenteredParallelDistance(localSubFaceIdx, 0);
distances[1] = ownScvf.cellCenteredParallelDistance(oppositeSubFaceIdx, 0);
- if(ownScvf.hasParallelNeighbor(localSubFaceIdx, 0))
+ if (ownScvf.hasParallelNeighbor(localSubFaceIdx, 0))
distances[2] = ownScvf.pairData(localSubFaceIdx).parallelCellWidths[0];
else
distances[2] = ownScvf.area() / 2.0;
@@ -592,10 +586,13 @@ private:
if (lateralFaceHasDirichletPressure)
return velocitySelf;
- const auto ghostFace = makeParallelGhostFace_(scvf, localSubFaceIdx);
if (lateralFaceHasBJS)
return problem.bjsVelocity(element, scvf, normalFace, localSubFaceIdx, velocitySelf);
- return problem.dirichlet(element, ghostFace)[Indices::velocity(scvf.directionIndex())];
+ else
+ {
+ const auto ghostFace = makeParallelGhostFace_(scvf, localSubFaceIdx);
+ return problem.dirichlet(element, ghostFace)[Indices::velocity(scvf.directionIndex())];
+ }
}
/*!
@@ -633,10 +630,7 @@ private:
else if (bcTypes.isSymmetry() || bcTypes.isDirichlet(Indices::pressureIdx))
return parallelVelocity;
else if (bcTypes.isBJS(Indices::velocity(scvf.directionIndex())))
- {
- const SubControlVolumeFace ghostFace = makeParallelGhostFace_(scvf, localIdx);
return problem.bjsVelocity(boundaryElement, scvf, boundaryNormalFace, localIdx, parallelVelocity);
- }
else
{
// Neumann conditions are not well implemented
diff --git a/test/freeflow/navierstokes/kovasznay/params.input b/test/freeflow/navierstokes/kovasznay/params.input
index 0f47acc145b5673a089a530996221e5acf63b58a..52c4a9dc4e6c74bbb419b6795b833276855233eb 100644
--- a/test/freeflow/navierstokes/kovasznay/params.input
+++ b/test/freeflow/navierstokes/kovasznay/params.input
@@ -19,3 +19,6 @@ MaxRelativeShift = 1e-5
[Vtk]
WriteFaceData = false
+
+[Flux]
+UpwindWeight = 0.5
diff --git a/test/references/test_ff_navierstokes_angeli-reference.vtu b/test/references/test_ff_navierstokes_angeli-reference.vtu
index 8cb65572763a4b8adcb2f538e15f300a524d9ce8..1b25f9895446021d48eaec3a50308920d49484ba 100644
--- a/test/references/test_ff_navierstokes_angeli-reference.vtu
+++ b/test/references/test_ff_navierstokes_angeli-reference.vtu
@@ -8,207 +8,207 @@
-2.21788 -1.09715 0.00591258 1.0739 2.08998 3.03812 3.90337 4.67208 5.33213 5.87312 6.2865 6.56577
6.70651 6.70651 6.56577 6.2865 5.87312 5.33213 4.67208 3.90337 3.03812 2.08998 1.0739 0.00591258
-1.09715 -2.21788 -3.33862 -4.44168 -5.50967 -6.52574 -7.47388 -8.33913 -9.10784 -9.7679 -10.3089 -10.7223
- -11.0015 -11.1423 -11.0029 -10.8489 -10.5615 -10.1367 -9.58282 -8.90968 -8.12851 -7.25207 -6.29448 -5.27107
- -4.19813 -3.09273 -1.97239 -0.854858 0.242196 1.30145 2.3062 3.24067 4.09024 4.84175 5.48371 6.00658
- 6.40298 6.66792 6.799 6.799 6.66792 6.40298 6.00658 5.48371 4.84175 4.09024 3.24067 2.3062
- 1.30145 0.242196 -0.854858 -1.97239 -3.09273 -4.19813 -5.27107 -6.29448 -7.25207 -8.12851 -8.90968 -9.58282
- -10.1367 -10.5615 -10.8489 -11.0029 -10.733 -10.6093 -10.318 -9.89056 -9.33492 -8.66055 -7.87859 -7.00172
- -6.04404 -5.02085 -3.94842 -2.84377 -1.72441 -0.608054 0.487665 1.54545 2.54865 3.48148 4.32938 5.07917
- 5.71936 6.24037 6.63475 6.89733 7.02538 7.02538 6.89733 6.63475 6.24037 5.71936 5.07917 4.32938
- 3.48148 2.54865 1.54545 0.487665 -0.608054 -1.72441 -2.84377 -3.94842 -5.02085 -6.04404 -7.00172 -7.87859
- -8.66055 -9.33492 -9.89056 -10.318 -10.6093 -10.733 -10.3494 -10.2582 -9.9636 -9.53385 -8.97657 -8.30106
- -7.5183 -6.64092 -5.68297 -4.65971 -3.58741 -2.48307 -1.36419 -0.248449 0.846514 1.90342 2.90559 3.83728
- 4.68387 5.43215 6.07059 6.58949 6.98124 7.24045 7.3641 7.3641 7.24045 6.98124 6.58949 6.07059
- 5.43215 4.68387 3.83728 2.90559 1.90342 0.846514 -0.248449 -1.36419 -2.48307 -3.58741 -4.65971 -5.68297
- -6.64092 -7.5183 -8.30106 -8.97657 -9.53385 -9.9636 -10.2582 -10.3494 -9.87623 -9.81659 -9.51937 -9.08774
- -8.52908 -7.85251 -7.06895 -6.19095 -5.23253 -4.20892 -3.13639 -2.03193 -0.913024 0.20263 1.29739 2.35397
- 3.35567 4.2867 5.13238 5.87945 6.51624 7.03292 7.42167 7.67684 7.79504 7.79504 7.67684 7.42167
- 7.03292 6.51624 5.87945 5.13238 4.2867 3.35567 2.35397 1.29739 0.20263 -0.913024 -2.03193 -3.13639
- -4.20892 -5.23253 -6.19095 -7.06895 -7.85251 -8.52908 -9.08774 -9.51937 -9.81659 -9.87623 -9.34329 -9.3117
- -9.0126 -8.57952 -8.01969 -7.34215 -6.55774 -5.67897 -4.71984 -3.69558 -2.62243 -1.5174 -0.397978 0.718123
- 1.81324 2.87005 3.87183 4.8027 5.64794 6.39415 7.02954 7.54408 7.9297 8.18043 8.29252 8.29252
- 8.18043 7.9297 7.54408 7.02954 6.39415 5.64794 4.8027 3.87183 2.87005 1.81324 0.718123 -0.397978
- -1.5174 -2.62243 -3.69558 -4.71984 -5.67897 -6.55774 -7.34215 -8.01969 -8.57952 -9.0126 -9.3117 -9.34329
- -8.78403 -8.7755 -8.47505 -8.04087 -7.48003 -6.80152 -6.01616 -5.13643 -4.17631 -3.15104 -2.07686 -0.970791
- 0.149657 1.26675 2.36278 3.4204 4.42281 5.35408 6.19937 6.94518 7.57952 8.09217 8.47478 8.721
- 8.82668 8.82668 8.721 8.47478 8.09217 7.57952 6.94518 6.19937 5.35408 4.42281 3.4204 2.36278
- 1.26675 0.149657 -0.970791 -2.07686 -3.15104 -4.17631 -5.13643 -6.01616 -6.80152 -7.48003 -8.04087 -8.47505
- -8.7755 -8.78403 -8.23358 -8.24225 -7.94087 -7.50579 -6.94401 -6.26448 -5.47799 -4.59705 -3.63562 -2.60895
- -1.53331 -0.425725 0.696265 1.81489 2.91241 3.9714 4.97502 5.90725 6.75315 7.49906 8.13283 8.64401
- 9.02392 9.26589 9.36528 9.36528 9.26589 9.02392 8.64401 8.13283 7.49906 6.75315 5.90725 4.97502
- 3.9714 2.91241 1.81489 0.696265 -0.425725 -1.53331 -2.60895 -3.63562 -4.59705 -5.47799 -6.26448 -6.94401
- -7.50579 -7.94087 -8.24225 -8.23358 -7.72655 -7.7463 -7.44428 -7.00843 -6.44569 -5.765 -4.97717 -4.09472
- -3.13163 -2.10316 -1.02561 0.0839757 1.20802 2.3287 3.42826 4.48919 5.49459 6.42834 7.2754 8.02197
- 8.65573 9.16597 9.54374 9.78198 9.87562 9.87562 9.78198 9.54374 9.16597 8.65573 8.02197 7.2754
- 6.42834 5.49459 4.48919 3.42826 2.3287 1.20802 0.0839757 -1.02561 -2.10316 -3.13163 -4.09472 -4.97717
- -5.765 -6.44569 -7.00843 -7.44428 -7.7463 -7.72655 -7.29478 -7.31997 -7.01751 -6.5809 -6.01709 -5.33506
- -4.54563 -3.66135 -2.69622 -1.66555 -0.585636 0.526416 1.653 2.77626 3.87835 4.94175 5.94945 6.88527
- 7.73404 8.48184 9.11618 9.62613 10.0025 10.2378 10.3266 10.3266 10.2378 10.0025 9.62613 9.11618
- 8.48184 7.73404 6.88527 5.94945 4.94175 3.87835 2.77626 1.653 0.526416 -0.585636 -1.66555 -2.69622
- -3.66135 -4.54563 -5.33506 -6.01709 -6.5809 -7.01751 -7.31997 -7.29478 -6.9654 -6.99157 -6.68875 -6.2513
- -5.68625 -5.00262 -4.2113 -3.32484 -2.35731 -1.32401 -0.24132 0.873641 2.00322 3.1295 4.23461 5.30093
- 6.31142 7.24979 8.10079 8.85038 9.48592 9.99628 10.372 10.6054 10.6906 10.6906 10.6054 10.372
- 9.99628 9.48592 8.85038 8.10079 7.24979 6.31142 5.30093 4.23461 3.1295 2.00322 0.873641 -0.24132
- -1.32401 -2.35731 -3.32484 -4.2113 -5.00262 -5.68625 -6.2513 -6.68875 -6.99157 -6.9654 -6.75912 -6.78376
- -6.48046 -6.04198 -5.47543 -4.78992 -3.99636 -3.10737 -2.13705 -1.10075 -0.0148687 1.10341 2.23639 3.36611
- 4.47463 5.5443 6.55799 7.49935 8.35305 9.10495 9.74228 10.2538 10.6299 10.8626 10.9458 10.9458
- 10.8626 10.6299 10.2538 9.74228 9.10495 8.35305 7.49935 6.55799 5.5443 4.47463 3.36611 2.23639
- 1.10341 -0.0148687 -1.10075 -2.13705 -3.10737 -3.99636 -4.78992 -5.47543 -6.04198 -6.48046 -6.78376 -6.75912
- -6.68888 -6.71203 -6.40791 -5.96808 -5.39972 -4.71198 -3.91584 -3.02395 -2.05046 -1.01076 0.0786886 1.20067
- 2.33743 3.47096 4.58327 5.65665 6.67391 7.61865 8.47547 9.23016 9.86989 10.3833 10.7607 10.994
- 11.077 11.077 10.994 10.7607 10.3833 9.86989 9.23016 8.47547 7.61865 6.67391 5.65665 4.58327
- 3.47096 2.33743 1.20067 0.0786886 -1.01076 -2.05046 -3.02395 -3.91584 -4.71198 -5.39972 -5.96808 -6.40791
- -6.71203 -6.68888 -6.75912 -6.78415 -6.48085 -6.04243 -5.47602 -4.79074 -3.99752 -3.10899 -2.13922 -1.10357
- -0.0184007 1.09913 2.23134 3.36032 4.46815 5.53719 6.55033 7.49125 8.34461 9.09626 9.73344 10.2449
- 10.6209 10.8536 10.9368 10.9368 10.8536 10.6209 10.2449 9.73344 9.09626 8.34461 7.49125 6.55033
- 5.53719 4.46815 3.36032 2.23134 1.09913 -0.0184007 -1.10357 -2.13922 -3.10899 -3.99752 -4.79074 -5.47602
- -6.04243 -6.48085 -6.78415 -6.75912 -6.9654 -6.99234 -6.68952 -6.25218 -5.6874 -5.00425 -4.21363 -3.32812
- -2.36175 -1.3298 -0.248597 0.864796 1.99278 3.11751 4.22117 5.28618 6.29554 7.23299 8.08328 8.83237
- 9.46757 9.97774 10.3534 10.5867 10.672 10.672 10.5867 10.3534 9.97774 9.46757 8.83237 8.08328
- 7.23299 6.29554 5.28618 4.22117 3.11751 1.99278 0.864796 -0.248597 -1.3298 -2.36175 -3.32812 -4.21363
- -5.00425 -5.6874 -6.25218 -6.68952 -6.99234 -6.9654 -7.29478 -7.3211 -7.01858 -6.5821 -6.01867 -5.33734
- -4.54899 -3.66616 -2.70283 -1.67424 -0.59663 0.512995 1.63712 2.75799 3.85784 4.91923 5.9252 6.85962
- 7.70732 8.45437 9.08823 9.59791 9.97413 10.2094 10.2982 10.2982 10.2094 9.97413 9.59791 9.08823
- 8.45437 7.70732 6.85962 5.9252 4.91923 3.85784 2.75799 1.63712 0.512995 -0.59663 -1.67424 -2.70283
- -3.66616 -4.54899 -5.33734 -6.01867 -6.5821 -7.01858 -7.3211 -7.29478 -7.72655 -7.74776 -7.44555 -7.00976
- -6.44745 -5.76767 -4.9813 -4.10084 -3.14023 -2.11465 -1.04027 0.0659615 1.18662 2.30402 3.4005 4.45869
- 5.46175 6.39362 7.23925 7.98485 8.61801 9.12796 9.50564 9.74389 9.83756 9.83756 9.74389 9.50564
- 9.12796 8.61801 7.98485 7.23925 6.39362 5.46175 4.45869 3.4005 2.30402 1.18662 0.0659615 -1.04027
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diff --git a/test/references/test_ff_navierstokes_kovasznay-reference.vtu b/test/references/test_ff_navierstokes_kovasznay-reference.vtu
index c0cc3674e4e6de7004e5db06228d935ce8c3e522..1d049c27a431a1a88a5c3bbd5d7e35800c19e4db 100644
--- a/test/references/test_ff_navierstokes_kovasznay-reference.vtu
+++ b/test/references/test_ff_navierstokes_kovasznay-reference.vtu
@@ -4,215 +4,215 @@
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diff --git a/test/references/test_ff_navierstokes_kovasznay_higherorder-reference.vtu b/test/references/test_ff_navierstokes_kovasznay_higherorder-reference.vtu
index 2c535c6561fa828f87cfb6be1d238c3b5272bc51..464245c06bad87edf6a487309e81641da7996b24 100644
--- a/test/references/test_ff_navierstokes_kovasznay_higherorder-reference.vtu
+++ b/test/references/test_ff_navierstokes_kovasznay_higherorder-reference.vtu
@@ -4,215 +4,215 @@
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