diff --git a/dumux/freeflow/navierstokes/staggered/localresidual.hh b/dumux/freeflow/navierstokes/staggered/localresidual.hh
index 485204b8d4ae494a32267c55c14e63be81e8b707..73821e002df834c0299a82d8d60803f882e94aea 100644
--- a/dumux/freeflow/navierstokes/staggered/localresidual.hh
+++ b/dumux/freeflow/navierstokes/staggered/localresidual.hh
@@ -302,17 +302,18 @@ protected:
             }
             else if(bcTypes.isNeumann(Indices::velocity(scvf.directionIndex())))
             {
-                // set a given Neumann flux for the face on the boundary itself
+                // the source term has already been accounted for, here we
+                // add a given Neumann flux for the face on the boundary itself ...
                 const auto extrusionFactor = elemVolVars[scvf.insideScvIdx()].extrusionFactor();
-                residual = problem.neumann(element, fvGeometry, elemVolVars, elemFaceVars, scvf)[Indices::velocity(scvf.directionIndex())]
+                residual += problem.neumann(element, fvGeometry, elemVolVars, elemFaceVars, scvf)[Indices::velocity(scvf.directionIndex())]
                                            * extrusionFactor * scvf.area();
 
-                // treat the remaining (frontal and lateral) faces of the staggered control volume
+                // ... and treat the fluxes of the remaining (frontal and lateral) faces of the staggered control volume
                 residual += computeFluxForFace(problem, element, scvf, fvGeometry, elemVolVars, elemFaceVars, elemFluxVarsCache);
             }
             else if(bcTypes.isSymmetry())
             {
-                // For symmetry boundary conditions, there is no flow accross the boundary and
+                // for symmetry boundary conditions, there is no flow accross the boundary and
                 // we therefore treat it like a Dirichlet boundary conditions with zero velocity
                 const Scalar velocity = elemFaceVars[scvf].velocitySelf();
                 const Scalar fixedValue = 0.0;
@@ -320,7 +321,8 @@ protected:
             }
             else if(bcTypes.isDirichlet(Indices::pressureIdx))
             {
-                // If none of the above conditions apply, we are at an "fixed pressure" boundary for which the velocity needs to be assembled
+                // if none of the above conditions apply, we are at an "fixed pressure" boundary for which the resdiual of the momentum balance needs to be assembled
+                // as if it where inside the domain and not on the boundary (source term has already been acounted for)
                 residual += computeFluxForFace(problem, element, scvf, fvGeometry, elemVolVars, elemFaceVars, elemFluxVarsCache);
             }
             else
diff --git a/dumux/multidomain/boundary/stokesdarcy/couplingdata.hh b/dumux/multidomain/boundary/stokesdarcy/couplingdata.hh
index 5846529cb7ae160a9c37a9cce145de35f5b81382..259d7da18e1e0406372e99e487246246b2ae190d 100644
--- a/dumux/multidomain/boundary/stokesdarcy/couplingdata.hh
+++ b/dumux/multidomain/boundary/stokesdarcy/couplingdata.hh
@@ -294,9 +294,14 @@ public:
         }
         else // use pressure reconstruction for single phase models
         {
+            // v = -K/mu * (gradP + rho*g)
             const Scalar velocity = stokesElemFaceVars[scvf].velocitySelf();
-            const Scalar pressureInterFace = scvf.directionSign() * velocity * stokesContext.volVars.viscosity(darcyPhaseIdx)/darcyPermeability(scvf) * (stokesContext.element.geometry().center() - scvf.center()).two_norm() + darcyPressure;
-            momentumFlux = pressureInterFace;
+            const Scalar mu = stokesContext.volVars.viscosity(darcyPhaseIdx);
+            const Scalar rho = stokesContext.volVars.density(darcyPhaseIdx);
+            const Scalar distance = (stokesContext.element.geometry().center() - scvf.center()).two_norm();
+            const Scalar g = couplingManager_.problem(darcyIdx).gravity()[scvf.directionIndex()];
+            const Scalar interfacePressure = ((scvf.directionSign() * velocity * (mu/darcyPermeability(scvf))) + rho * g) * distance + darcyPressure;
+            momentumFlux = interfacePressure;
         }
 
         // normalize pressure
diff --git a/dumux/multidomain/boundary/stokesdarcy/couplingmanager.hh b/dumux/multidomain/boundary/stokesdarcy/couplingmanager.hh
index d218acd81a0cb2ec7ddde18bccdbd9690b54a9cf..04b704f33e35d9634304f8240fa73d4d43b5a42a 100644
--- a/dumux/multidomain/boundary/stokesdarcy/couplingmanager.hh
+++ b/dumux/multidomain/boundary/stokesdarcy/couplingmanager.hh
@@ -30,6 +30,8 @@
 #include <utility>
 #include <memory>
 
+#include <dune/common/float_cmp.hh>
+#include <dune/common/exceptions.hh>
 #include <dumux/common/properties.hh>
 #include <dumux/multidomain/staggeredcouplingmanager.hh>
 
@@ -119,7 +121,6 @@ public:
 
     using ParentType::couplingStencil;
     using ParentType::updateCouplingContext;
-    using DarcyGridVariables = GridVariables<2>;
     using CouplingData = StokesDarcyCouplingData<MDTraits, StokesDarcyCouplingManager<MDTraits>>;
 
     //! Constructor
@@ -137,6 +138,9 @@ public:
               std::shared_ptr<const Problem<darcyIdx>> darcyProblem,
               const SolutionVector& curSol)
     {
+        if(Dune::FloatCmp::ne(stokesProblem->gravity(), darcyProblem->gravity()))
+            DUNE_THROW(Dune::InvalidStateException, "Both models must use the same gravity vector");
+
         ParentType::init(std::make_tuple(stokesProblem, stokesProblem, darcyProblem));
         this->curSol() = curSol;
         couplingData_ = std::make_shared<CouplingData>(*this);
diff --git a/test/references/test_stokes1p2cnidarcy2p2cnihorizontal_darcy-reference.vtu b/test/references/test_stokes1p2cnidarcy2p2cnihorizontal_darcy-reference.vtu
index a4ebe346a5e3b202f1be4196c025c1cfa516ff19..8172835a1cca9873dba33103abe348141637ad2a 100644
--- a/test/references/test_stokes1p2cnidarcy2p2cnihorizontal_darcy-reference.vtu
+++ b/test/references/test_stokes1p2cnidarcy2p2cnihorizontal_darcy-reference.vtu
@@ -2,31 +2,31 @@
 <VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
   <UnstructuredGrid>
     <Piece NumberOfCells="64" NumberOfPoints="81">
-      <CellData Scalars="S_n" Vectors="velocity_liquid (m/s)">
-        <DataArray type="Float32" Name="S_n" NumberOfComponents="1" format="ascii">
-          0.231386 0.231386 0.231387 0.231387 0.231387 0.231387 0.231387 0.231387 0.816991 0.816991 0.816993 0.816994
-          0.816995 0.816997 0.816997 0.816998 0.937394 0.937394 0.937393 0.937393 0.937393 0.937393 0.937393 0.937393
-          0.966181 0.966171 0.966161 0.966154 0.966149 0.966145 0.966142 0.966141 0.977391 0.977355 0.977326 0.977304
-          0.977287 0.977273 0.977264 0.977261 0.983867 0.983784 0.983724 0.983681 0.983647 0.983619 0.983599 0.983594
-          0.990183 0.989914 0.989734 0.989612 0.989514 0.989436 0.989376 0.989364 1 1 1 1
-          1 1 1 1
+      <CellData Scalars="porosity" Vectors="velocity_liquid (m/s)">
+        <DataArray type="Float32" Name="porosity" NumberOfComponents="1" format="ascii">
+          0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41
+          0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41
+          0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41
+          0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41
+          0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41
+          0.41 0.41 0.41 0.41
+        </DataArray>
+        <DataArray type="Float32" Name="pc" NumberOfComponents="1" format="ascii">
+          1346.28 1346.28 1346.28 1346.28 1346.28 1346.28 1346.28 1346.28 2053.9 2053.9 2053.9 2053.9
+          2053.91 2053.91 2053.91 2053.91 2526.12 2526.11 2526.11 2526.11 2526.11 2526.11 2526.11 2526.11
+          2849.26 2849.08 2848.92 2848.8 2848.71 2848.63 2848.58 2848.57 3100.58 3099.48 3098.61 3097.95
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+          3721.5 3705.55 3694.95 3687.67 3681.92 3677.26 3673.76 3673.04 4302.49 4302.49 4302.49 4302.49
+          4302.49 4302.49 4302.49 4302.49
         </DataArray>
         <DataArray type="Float32" Name="S_w" NumberOfComponents="1" format="ascii">
-          0.768614 0.768614 0.768613 0.768613 0.768613 0.768613 0.768613 0.768613 0.183009 0.183009 0.183007 0.183006
+          0.768614 0.768614 0.768614 0.768613 0.768613 0.768613 0.768613 0.768613 0.183009 0.183009 0.183007 0.183006
           0.183005 0.183004 0.183003 0.183002 0.0626056 0.0626064 0.0626069 0.062607 0.0626069 0.0626068 0.0626066 0.0626065
           0.0338188 0.0338293 0.0338386 0.0338457 0.0338511 0.0338553 0.0338582 0.0338591 0.0226087 0.0226453 0.0226743 0.0226961
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-          0.0098168 0.0100864 0.0102655 0.0103884 0.0104857 0.0105644 0.0106236 0.0106356 0 0 0 0
+          0.0227132 0.0227267 0.0227364 0.022739 0.0161331 0.0162165 0.0162761 0.0163191 0.0163533 0.0163808 0.0164012 0.0164059
+          0.00981681 0.0100864 0.0102655 0.0103884 0.0104857 0.0105644 0.0106236 0.0106356 0 0 0 0
           0 0 0 0
         </DataArray>
-        <DataArray type="Float32" Name="p_n" NumberOfComponents="1" format="ascii">
-          100002 100002 100002 100002 100002 100002 100002 100002 100002 100002 100002 100002
-          100002 100002 100002 100002 100001 100001 100001 100001 100001 100001 100001 100001
-          100001 100001 100001 100001 100001 100001 100001 100001 100000 100000 100000 100000
-          100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000
-          100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000
-          100000 100000 100000 100000
-        </DataArray>
         <DataArray type="Float32" Name="p_w" NumberOfComponents="1" format="ascii">
           98656.1 98656.1 98656.1 98656.1 98656.1 98656.1 98656.1 98656.1 97947.7 97947.7 97947.7 97947.7
           97947.7 97947.7 97947.7 97947.7 97474.9 97474.9 97474.9 97474.9 97474.9 97474.9 97474.9 97474.9
@@ -35,14 +35,6 @@
           96278.6 96294.5 96305.1 96312.4 96318.2 96322.8 96326.3 96327 95697.5 95697.5 95697.5 95697.5
           95697.5 95697.5 95697.5 95697.5
         </DataArray>
-        <DataArray type="Float32" Name="pc" NumberOfComponents="1" format="ascii">
-          1346.28 1346.28 1346.28 1346.28 1346.28 1346.28 1346.28 1346.28 2053.9 2053.9 2053.9 2053.9
-          2053.91 2053.91 2053.91 2053.91 2526.12 2526.11 2526.11 2526.11 2526.11 2526.11 2526.11 2526.11
-          2849.26 2849.08 2848.92 2848.8 2848.71 2848.63 2848.58 2848.57 3100.58 3099.48 3098.61 3097.95
-          3097.44 3097.04 3096.75 3096.67 3352.96 3348.7 3345.68 3343.5 3341.79 3340.41 3339.39 3339.16
-          3721.5 3705.55 3694.95 3687.67 3681.92 3677.26 3673.76 3673.04 4302.49 4302.49 4302.49 4302.49
-          4302.49 4302.49 4302.49 4302.49
-        </DataArray>
         <DataArray type="Float32" Name="rho_w" NumberOfComponents="1" format="ascii">
           999.385 999.387 999.389 999.392 999.395 999.397 999.399 999.4 999.352 999.355 999.36 999.367
           999.373 999.379 999.383 999.385 999.308 999.315 999.327 999.34 999.352 999.363 999.37 999.373
@@ -51,14 +43,6 @@
           999.123 999.192 999.25 999.289 999.321 999.346 999.364 999.37 271.631 328.146 369.108 400.775
           427.636 450.858 469.655 473.181
         </DataArray>
-        <DataArray type="Float32" Name="rho_n" NumberOfComponents="1" format="ascii">
-          1.21091 1.21095 1.21104 1.21115 1.21127 1.21137 1.21145 1.21149 1.20961 1.20973 1.20993 1.21018
-          1.21043 1.21065 1.21081 1.21089 1.20787 1.20816 1.20862 1.20913 1.20961 1.21002 1.2103 1.21044
-          1.20607 1.20665 1.20746 1.20829 1.20904 1.20964 1.21005 1.21025 1.2044 1.2054 1.2066 1.20773
-          1.2087 1.20947 1.20999 1.21022 1.20295 1.20445 1.20601 1.20737 1.20851 1.20941 1.21002 1.21025
-          1.20176 1.20376 1.20561 1.20714 1.2084 1.20939 1.21008 1.21031 1.20645 1.20833 1.20996 1.2113
-          1.21238 1.21324 1.21382 1.21399
-        </DataArray>
         <DataArray type="Float32" Name="mob_w" NumberOfComponents="1" format="ascii">
           343.952 343.852 343.673 343.445 343.206 342.991 342.83 342.744 4.84623 4.8427 4.83658 4.8292
           4.82183 4.81545 4.81082 4.80841 0.196025 0.195688 0.195146 0.194538 0.193965 0.193492 0.19316 0.192991
@@ -67,36 +51,92 @@
           0.000176098 0.000203354 0.000222036 0.000234824 0.000245161 0.000253738 0.000260397 0.000261626 0 0 0 0
           0 0 0 0
         </DataArray>
+        <DataArray type="Float32" Name="S_n" NumberOfComponents="1" format="ascii">
+          0.231386 0.231386 0.231387 0.231387 0.231387 0.231387 0.231387 0.231387 0.816991 0.816991 0.816993 0.816994
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+          0.990183 0.989914 0.989734 0.989612 0.989514 0.989436 0.989376 0.989364 1 1 1 1
+          1 1 1 1
+        </DataArray>
+        <DataArray type="Float32" Name="p_n" NumberOfComponents="1" format="ascii">
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+          100002 100002 100002 100002 100001 100001 100001 100001 100001 100001 100001 100001
+          100001 100001 100001 100001 100001 100001 100001 100001 100000 100000 100000 100000
+          100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000
+          100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000
+          100000 100000 100000 100000
+        </DataArray>
+        <DataArray type="Float32" Name="rho_n" NumberOfComponents="1" format="ascii">
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+        </DataArray>
         <DataArray type="Float32" Name="mob_n" NumberOfComponents="1" format="ascii">
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