FEAT: Added the Jacobians of the balance of mass

UCBoulder · Jun 11, 2024 · 2e43606 · 2e43606
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diff --git a/src/cpp/tardigrade_balance_of_mass.cpp b/src/cpp/tardigrade_balance_of_mass.cpp
@@ -37,6 +37,45 @@ namespace tardigradeBalanceEquations{
 
         }
 
+        void computeBalanceOfMass( const floatType   &density,  const floatType         &density_dot,       const floatVector &density_gradient,
+                                   const floatVector &velocity, const secondOrderTensor &velocity_gradient, floatType &mass_change_rate, 
+                                   floatType   &dCdRho, floatType         &dCdRhoDot, floatVector &dCdGradRho,
+                                   floatVector &dCdV,   secondOrderTensor &dCdGradV ){
+            /*!
+             * Compute the value of the balance of mass returning the value of the mass change rate including the Jacobians
+             * 
+             * \f$ \frac{\partial \rho}{\partial t} + \left( \rho v_i \right)_{,i} = c \f$
+             *
+             * \param &density: The value of the density \f$ \rho \f$
+             * \param &density_dot: The value of the partial derivative of the density \f$ \frac{\partial \rho}{\partial t} \f$
+             * \param &density_gradient: The value of the spatial gradient of the density \f$ \rho_{,i} \f$
+             * \param &velocity: The value of the velocity \f$ v_i \f$
+             * \param &velocity_gradient: The value of the spatial gradient of the velocity \f$ v_{i,j} \f$
+             * \param &mass_change_rate: The rate of change of the mass \f$ c \f$
+             */
+
+            computeBalanceOfMass( density, density_dot, density_gradient, velocity, velocity_gradient, mass_change_rate );
+
+            dCdRho = 0;
+
+            dCdRhoDot = 1;
+
+            dCdGradRho = velocity;
+
+            dCdV = density_gradient;
+
+            std::fill( std::begin( dCdGradV ), std::end( dCdGradV ), 0 );
+
+            for ( unsigned int i = 0; i < dim; i++ ){
+
+                dCdRho += velocity_gradient[ dim * i + i ];
+
+                dCdGradV[ dim * i + i ] = density;
+
+            }
+
+        }
+
     }
 
 }

diff --git a/src/cpp/tardigrade_balance_of_mass.h b/src/cpp/tardigrade_balance_of_mass.h
@@ -31,6 +31,11 @@ namespace tardigradeBalanceEquations{
         void computeBalanceOfMass( const floatType   &density,  const floatType         &density_dot,       const floatVector &density_gradient,
                                    const floatVector &velocity, const secondOrderTensor &velocity_gradient, floatType &mass_change_rate );
 
+        void computeBalanceOfMass( const floatType   &density,  const floatType         &density_dot,       const floatVector &density_gradient,
+                                   const floatVector &velocity, const secondOrderTensor &velocity_gradient, floatType &mass_change_rate,
+                                   floatType   &dCdRho, floatType         &dCdRhoDot, floatVector &dCdGradRho,
+                                   floatVector &dCdV,   secondOrderTensor &dCdGradV );
+
     }
 
 }

diff --git a/src/cpp/tests/test_tardigrade_balance_of_mass.cpp b/src/cpp/tests/test_tardigrade_balance_of_mass.cpp
@@ -71,5 +71,134 @@ BOOST_AUTO_TEST_CASE( test_computeBalanceOfMass, * boost::unit_test::tolerance(
 
     BOOST_TEST( answer == result );
 
-}
+    floatType dCdRho, dCdRhoDot;
+
+    floatVector dCdGradRho, dCdV;
+
+    secondOrderTensor dCdGradV;
+
+    tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, density_dot, density_gradient, velocity, velocity_gradient, result,
+                                                                     dCdRho,  dCdRhoDot,   dCdGradRho      , dCdV,     dCdGradV );
+
+    BOOST_TEST( answer == result );
+
+    floatType eps = 1e-6;
+
+    // Derivative w.r.t. density
+    for ( unsigned int i = 0; i < 1; i++ ){
+
+        floatType delta = eps * std::fabs( density ) + eps;
+
+        floatType xp = density + delta;
+
+        floatType xm = density - delta;
+
+        floatType vp;
+
+        floatType vm;
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( xp, density_dot, density_gradient, velocity, velocity_gradient, vp );
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( xm, density_dot, density_gradient, velocity, velocity_gradient, vm );
+
+        BOOST_TEST( dCdRho == ( vp - vm ) / ( 2 * delta ) );
+
+    }
+
+    // Derivative w.r.t. density dot
+    for ( unsigned int i = 0; i < 1; i++ ){
+
+        floatType delta = eps * std::fabs( density_dot ) + eps;
+
+        floatType xp = density_dot + delta;
+
+        floatType xm = density_dot - delta;
+
+        floatType vp;
+
+        floatType vm;
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, xp, density_gradient, velocity, velocity_gradient, vp );
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, xm, density_gradient, velocity, velocity_gradient, vm );
+
+        BOOST_TEST( dCdRhoDot == ( vp - vm ) / ( 2 * delta ) );
+
+    }
+
+    // Derivative w.r.t. density gradient
+    for ( unsigned int i = 0; i < 3; i++ ){
+
+        floatType delta = eps * std::fabs( density_gradient[ i ] ) + eps;
+
+        floatVector xp = density_gradient;
+
+        floatVector xm = density_gradient;
+
+        xp[ i ] += delta;
+
+        xm[ i ] -= delta;
 
+        floatType vp;
+
+        floatType vm;
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, density_dot, xp, velocity, velocity_gradient, vp );
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, density_dot, xm, velocity, velocity_gradient, vm );
+
+        BOOST_TEST( dCdGradRho[ i ] == ( vp - vm ) / ( 2 * delta ) );
+
+    }
+
+    // Derivative w.r.t. velocity
+    for ( unsigned int i = 0; i < 3; i++ ){
+
+        floatType delta = eps * std::fabs( velocity[ i ] ) + eps;
+
+        floatVector xp = velocity;
+
+        floatVector xm = velocity;
+
+        xp[ i ] += delta;
+
+        xm[ i ] -= delta;
+
+        floatType vp;
+
+        floatType vm;
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, density_dot, density_gradient, xp, velocity_gradient, vp );
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, density_dot, density_gradient, xm, velocity_gradient, vm );
+
+        BOOST_TEST( dCdV[ i ] == ( vp - vm ) / ( 2 * delta ) );
+
+    }
+
+    // Derivative w.r.t. velocity gradient
+    for ( unsigned int i = 0; i < 9; i++ ){
+
+        floatType delta = eps * std::fabs( velocity_gradient[ i ] ) + eps;
+
+        secondOrderTensor xp = velocity_gradient;
+
+        secondOrderTensor xm = velocity_gradient;
+
+        xp[ i ] += delta;
+
+        xm[ i ] -= delta;
+
+        floatType vp;
+
+        floatType vm;
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, density_dot, density_gradient, velocity, xp, vp );
+
+        tardigradeBalanceEquations::balanceOfMass::computeBalanceOfMass( density, density_dot, density_gradient, velocity, xm, vm );
+
+        BOOST_TEST( dCdGradV[ i ] == ( vp - vm ) / ( 2 * delta ) );
+
+    }
+
+}