add the neumann option to the angeli test

test/freeflow/navierstokes/angeli/problem.hh

@@ -79,6 +79,7 @@ public:
     : ParentType(gridGeometry, couplingManager)
     {
         kinematicViscosity_ = getParam<Scalar>("Component.LiquidKinematicViscosity", 1.0);
+        useNeumann_ = getParam<bool>("Problem.UseNeumann", false);
         useQuad_ = getParam<bool>("Problem.UseQuad", false);
     }
 
@@ -105,7 +106,14 @@ public:
         BoundaryTypes values;
 
         if constexpr (ParentType::isMomentumProblem())
+        {
+            static constexpr Scalar eps = 1e-8;
+            if (useNeumann_ && (globalPos[0] > this->gridGeometry().bBoxMax()[0] - eps ||
+                                globalPos[1] > this->gridGeometry().bBoxMax()[1] - eps))
+                values.setAllNeumann();
+            else
                 values.setAllDirichlet();
+        }
         else
             values.setAllNeumann();
 
@@ -134,6 +142,8 @@ public:
 
         // We don't need internal Dirichlet conditions if a Neumann BC is set for the momentum balance (which accounts for the pressure).
         // If only Dirichlet BCs are set for the momentum balance, fix the pressure at some cells such that the solution is fully defined.
+        if (!useNeumann_)
+        {
             auto fvGeometry = localView(this->gridGeometry());
             fvGeometry.bindElement(element);
 
@@ -146,6 +156,7 @@ public:
 
             if (isAtBoundary(fvGeometry))
                 values.set(Indices::pressureIdx);
+        }
 
         return values;
     }
@@ -177,6 +188,51 @@ public:
             return analyticalSolution(scvf.center(), time_);
     }
 
+    /*!
+     * \brief Evaluates the boundary conditions for a Neumann control volume.
+     *
+     * \param element The element for which the Neumann boundary condition is set
+     * \param fvGeometry The fvGeometry
+     * \param elemVolVars The element volume variables
+     * \param elemFaceVars The element face variables
+     * \param scvf The boundary sub control volume face
+     */
+    template<class ElementVolumeVariables, class ElementFluxVariablesCache>
+    NumEqVector neumann(const Element& element,
+                        const FVElementGeometry& fvGeometry,
+                        const ElementVolumeVariables& elemVolVars,
+                        const ElementFluxVariablesCache& elemFluxVarsCache,
+                        const SubControlVolumeFace& scvf) const
+    {
+        NumEqVector values(0.0);
+
+        if constexpr (!ParentType::isMomentumProblem())
+        {
+            const auto insideDensity = elemVolVars[scvf.insideScvIdx()].density();
+            values[Indices::conti0EqIdx] = this->faceVelocity(element, fvGeometry, scvf) * insideDensity * scvf.unitOuterNormal();
+        }
+        else
+        {
+            using std::sin;
+            using std::cos;
+            Dune::FieldMatrix<Scalar, 2, 2> momentumFlux(0.0);
+            const auto x = scvf.ipGlobal()[0];
+            const auto y = scvf.ipGlobal()[1];
+            const Scalar mu = kinematicViscosity_;
+            const Scalar t = time_;
+            momentumFlux[0][0] = M_PI*M_PI *(-4.0*mu*exp(10.0*M_PI*M_PI*mu*t)*sin(M_PI*x)*sin(2*M_PI*y) + (4.0*sin(2*M_PI*y)*sin(2*M_PI*y)*cos(M_PI*x)*cos(M_PI*x) - 1.0*cos(2*M_PI*x) - 0.25*cos(4*M_PI*y))*exp(5.0*M_PI*M_PI*mu*t))*exp(-15.0*M_PI*M_PI*mu*t);
+            momentumFlux[0][1] = M_PI*M_PI *( 3.0*mu*exp(10.0*M_PI*M_PI*mu*t) - 2.0*exp(5.0*M_PI*M_PI*mu*t)*sin(M_PI*x)*sin(2*M_PI*y))*exp(-15.0*M_PI*M_PI*mu*t)*cos(M_PI*x)*cos(2*M_PI*y);
+            momentumFlux[1][0] = M_PI*M_PI *( 3.0*mu*exp(10.0*M_PI*M_PI*mu*t) - 2.0*exp(5.0*M_PI*M_PI*mu*t)*sin(M_PI*x)*sin(2*M_PI*y))*exp(-15.0*M_PI*M_PI*mu*t)*cos(M_PI*x)*cos(2*M_PI*y);
+            momentumFlux[1][1] = M_PI*M_PI *( 4.0*mu*exp(10.0*M_PI*M_PI*mu*t)*sin(M_PI*x)*sin(2*M_PI*y) + (sin(M_PI*x)*sin(M_PI*x)*cos(2*M_PI*y)*cos(2*M_PI*y) - 1.0*cos(2*M_PI*x) - 0.25*cos(4*M_PI*y))*exp(5.0*M_PI*M_PI*mu*t))*exp(-15.0*M_PI*M_PI*mu*t);
+
+            const auto normal = scvf.unitOuterNormal();
+            momentumFlux.mv(normal, values);
+        }
+
+        return values;
+    }
+
+
 
     /*!
      * \brief Returns the analytical solution of the problem at a given time and position.
@@ -282,6 +338,7 @@ private:
 
     Scalar kinematicViscosity_;
     Scalar time_ = 0.0;
+    bool useNeumann_;
     bool useQuad_;
 };
 } // end namespace Dumux