inline Real
OneDFSIPhysics::dAdP( const Real& P, const Real& timeStep, const UInt& iNode, const bool& elasticExternalNodes ) const
{
if ( !M_dataPtr->viscoelasticWall() || ( ( iNode == 0 || iNode == M_dataPtr->numberOfNodes() - 1 ) && elasticExternalNodes ) )
{
return M_dataPtr->area0( iNode ) / ( M_dataPtr->beta0( iNode ) * M_dataPtr->beta1( iNode ) )
* OneDFSI::pow10( 1 + ( P - externalPressure() )
/ M_dataPtr->beta0( iNode ), 1 / M_dataPtr->beta1( iNode ) - 1 );
}
else
{
// Finite difference approach
return ( fromPToA( P + M_dataPtr->jacobianPerturbationStress(), timeStep, iNode, elasticExternalNodes ) - fromPToA( P, timeStep, iNode, elasticExternalNodes ) )
/ M_dataPtr->jacobianPerturbationStress();
}
}
inline Real
OneDFSIPhysics::elasticPressure( const Real& A, const UInt& iNode ) const
{
return ( M_dataPtr->beta0( iNode ) * ( OneDFSI::pow05( A/M_dataPtr->area0( iNode ), M_dataPtr->beta1( iNode ) ) - 1 ) );
}
// ===================================================
// Inline methods
// ===================================================
inline Real
OneDFSIPhysics::celerity0( const UInt& iNode ) const
{
return std::sqrt( M_dataPtr->beta0( iNode ) * M_dataPtr->beta1( iNode ) / M_dataPtr->densityRho() );
}
inline Real
OneDFSIPhysics::dPdAelastic( const Real& A, const UInt& iNode ) const
{
return M_dataPtr->beta0( iNode ) * M_dataPtr->beta1( iNode ) * OneDFSI::pow05( A / M_dataPtr->area0( iNode ), M_dataPtr->beta1( iNode ) ) / A;
}
// ===================================================
// Inline conversion methods
// ===================================================
inline Real
OneDFSIPhysics::fromPToA( const Real& P, const Real& timeStep, const UInt& iNode, const bool& elasticExternalNodes ) const
{
if ( !M_dataPtr->viscoelasticWall() || ( ( iNode == 0 || iNode == M_dataPtr->numberOfNodes() - 1 ) && elasticExternalNodes ) )
return ( M_dataPtr->area0( iNode ) * OneDFSI::pow20( ( P - externalPressure() ) / M_dataPtr->beta0( iNode ) + 1, 1 / M_dataPtr->beta1( iNode ) ) );
else
{
// Newton method to solve the non linear equation
Real tolerance(1e-6);
Real maxIT(100);
UInt i(0);
Real A( M_dataPtr->area0( iNode ) );
Real newtonUpdate(0);
for ( ; i < maxIT ; ++i )
{
if ( std::abs( pressure( A, timeStep, iNode, elasticExternalNodes ) - P ) < tolerance )
break;
newtonUpdate = ( pressure( A, timeStep, iNode, elasticExternalNodes ) - P ) / dPdA( A, timeStep, iNode, elasticExternalNodes );
if ( A - newtonUpdate <= 0 )
A /= 2.0; // Bisection
else
A -= newtonUpdate; // Newton
}
if ( i == maxIT )
{
std::cout << "!!! Warning: conversion fromPToA below tolerance !!! " << std::endl;
std::cout << "Tolerance: " << tolerance << "; Residual: " << std::abs( pressure( A, timeStep, iNode, elasticExternalNodes ) - P ) << std::endl;
}
return A;
}
}