Functions
double	null (const double &t)
	Null function. More...

double	angle (const double &t)
	Angular position as a function of time t. More...

double	velocity (const double &t)
	Angular velocity as function of time t. More...

double	acceleration (const double &t)
	Angular acceleration as a function of time t (should always be zero) More...

Detailed Description

Exact solution for the rotation of an ellipse in unbounded shear flow as computed by Jeffery (1922)

Function Documentation

◆ acceleration()

double Jeffery_Solution::acceleration ( const double & t )

Angular acceleration as a function of time t (should always be zero)

  {
   const double a = Problem_Parameter::A;
   const double b = Problem_Parameter::A;
  
   //Get the angle and velocity
   double chi = angle(t);
   double chi_dot = velocity(t);
  
   //Now return the acceleration
   return 2.0*(a*a - b*b)*(sin(chi)*cos(chi))*chi_dot/(a*a + b*b);
  }

References a, Problem_Parameter::A, angle(), b, cos(), sin(), plotPSD::t, and velocity().

Referenced by ClosedCSCWalls::actionsAfterTimeStep(), and UnstructuredImmersedEllipseProblem< ELEMENT >::output_exact_solution().

◆ angle()

double Jeffery_Solution::angle ( const double & t )

Angular position as a function of time t.

  {
   const double a = Problem_Parameter::A;
   const double b = Problem_Parameter::B;
   
   return atan((b/a)*tan((a*b*t)/(b*b + a*a)));
  }

References a, Problem_Parameter::A, Eigen::bfloat16_impl::atan(), b, Problem_Parameter::B, plotPSD::t, and Eigen::bfloat16_impl::tan().

Referenced by acceleration(), LawinenBox::actionsBeforeTimeStep(), VerticalMixerAngledBlades::addPrettyBlades(), ChuteWithWedge::addWedge(), alignedboxNonIntegralRotatable(), CircularPenetratorElement::centre(), oomph::OcTree::construct_rotation_matrix(), GpuHelper::drawVector(), GpuHelper::drawVectorBox(), Quaternion::fromAxisAndAngle(), HorizontalBaseScrew::getDistanceAndNormal(), Eigen::internal::idrs(), main(), objectivenessTest(), Eigen::internal::omega(), UnstructuredImmersedEllipseProblem< ELEMENT >::output_exact_solution(), DPMBase::readNextDataFile(), oomph::RotatableRefineableCubicMesh< ELEMENT >::RotatableRefineableCubicMesh(), oomph::Rotateable< ELEMENT >::rotate(), Rotateable< ELEMENT >::rotate(), rotate2D(), rotate2DIntegral(), rotate3DZAxis(), rotate3DZAxisIntegral(), rotate4DZWAxis(), CylinderInsertionBoundary::rotateBoundary(), CircularPeriodicBoundary::rotateParticle(), ClumpParticle::rotatePrincipalDirections(), CircularPenetratorElement::set_angle(), ChutePeriodic::set_chute_parameters(), Eigen::IDRS< MatrixType_, Preconditioner_ >::setAngle(), ChuteWithHopper::setHopper(), ConstantMassFlowMaserBoundaryMixedSpeciesSelfTest::setupInitialConditions(), ConstantMassFlowMaserSelfTest::setupInitialConditions(), test2dHyperbolicRotation(), test2dRotation(), test3dRotation(), TestRefineableCubicMesh< ELEMENT >::TestRefineableCubicMesh(), TestRefineablePoissonProblem< ELEMENT >::TestRefineablePoissonProblem(), TestRefineableRectangularQuadMesh< ELEMENT >::TestRefineableRectangularQuadMesh(), Trackball::track(), transformations(), velocity(), HorizontalBaseScrew::writeVTK(), ScrewsymmetricIntersectionOfWalls::writeVTK(), and AxisymmetricIntersectionOfWalls::writeVTK().

◆ null()

double Jeffery_Solution::null ( const double & t )

Null function.

95 {return 0.0;}

◆ velocity()

double Jeffery_Solution::velocity ( const double & t )

Angular velocity as function of time t.

  {
   const double a = Problem_Parameter::A;
   const double b = Problem_Parameter::B;
  
   //Get the angle
   double chi = angle(t);
  
   //Now return the velocity
   return (a*a*sin(chi)*sin(chi) + b*b*cos(chi)*cos(chi))/(a*a + b*b);
  }

References a, Problem_Parameter::A, angle(), b, Problem_Parameter::B, cos(), sin(), and plotPSD::t.