Function object for tests/ins/jeffery_hamel responsible for setting the exact value of the velocity and pressure variables. More...

#include <WedgeFunction.h>

Inheritance diagram for WedgeFunction:

[legend]

Public Member Functions
	WedgeFunction (const InputParameters &parameters)

virtual Real	value (Real t, const Point &p) const override

Protected Attributes
const Real	_alpha_radians
	The half-angle of the wedge, stored in radians. More...

const Real	_Re
	The Reynolds number, (u_max(r) * r * alpha) / nu. More...

const unsigned int	_var_num
	The variable (vel_x==0, vel_y==1, p==2) being computed by this instance of WedgeFunction. More...

const Real	_mu
	The (constant) dynamic viscosity of the fluid. Usually specified in [GlobalParams]. More...

const Real	_rho
	The (constant) density of the fluid. Usually specified in [GlobalParams]. More...

const Real	_nu
	The kinematic viscosity = mu/rho. More...

const Real	_K
	The constant K from the Jeffery-Hamel solution, defined by: K = -f - 1/(4 * alpha^2) * (alpha * Re * f^2 + f'') which is required for computing the exact pressure: More...

const Real	_lambda
	The quantity u_max(r) * r, which is constant for this problem, and can be computed given the Reynolds number, nu, and alpha according to: lambda = _Re * _nu / _alpha_radians. More...

const Real	_p_star
	The pressure constant, whose value is determined from the pressure pin. More...

const Function &	_f
	The pre-computed semi-analytic exact solution f(theta) as a PiecewiseLinear function. More...

Detailed Description

Function object for tests/ins/jeffery_hamel responsible for setting the exact value of the velocity and pressure variables.

Inherits from FunctionInterface (similarly to CompositeFunction) so that it can couple to a PiecewiseLinear function which corresponds to the non-dimensional semi-analytic solution on the domain [0,1]. This function is responsible for scaling and mapping the semi-analytic solution values to the actual velocities and pressure used in the problem.

Definition at line 30 of file WedgeFunction.h.

Constructor & Destructor Documentation

◆ WedgeFunction()

WedgeFunction::WedgeFunction ( const InputParameters & parameters )

Definition at line 38 of file WedgeFunction.C.

   : Function(parameters),
     FunctionInterface(this),
     _alpha_radians(libMesh::pi * (getParam<Real>("alpha_degrees") / 180.)),
     _Re(getParam<Real>("Re")),
     _var_num(getParam<unsigned int>("var_num")),
     _mu(getParam<Real>("mu")),
     _rho(getParam<Real>("rho")),
     _nu(_mu / _rho),
     _K(getParam<Real>("K")),
     _lambda(_Re * _nu / _alpha_radians),
     _p_star(-2 * _mu * _lambda * (1 + _K)),
     _f(getFunction("f"))
 {
 }

Member Function Documentation

◆ value()

Real WedgeFunction::value	(	Real	t,
		const Point &	p
	)		const

overridevirtual

Definition at line 55 of file WedgeFunction.C.

 {
   const Real r = std::sqrt(p(0) * p(0) + p(1) * p(1));
   const Real theta = std::atan2(p(1), p(0));
  
   // This is really unlikely to happen unless someone does something
   // very strange with their mesh.
   mooseAssert(r != 0., "The exact solution is singular at r=0.");
  
   // The "f" function is defined in terms of eta=theta/alpha, and it
   // is only defined for positive angles, since it is symmetric about
   // 0.
   const Real eta = std::abs(theta) / _alpha_radians;
  
   // We pass "eta" to the PiecewiseLinear function in place of "time",
   // plus a dummy Point which is not used.
   const Real f_value = _f.value(eta, _point_zero);
  
   // Vars 0 and 1 are the velocities.
   if (_var_num < 2)
   {
     // Converts the radial velocity vector to x and y components, respectively.
     const Real cs[2] = {std::cos(theta), std::sin(theta)};
  
     // Compute the centerline velocity for this r.
     const Real u_max = _lambda / r;
  
     // The true velocity value is simply u_max * f, times either
     // cos(theta) or sin(theta) to convert it to Cartesian coordinates.
     return u_max * f_value * cs[_var_num];
   }
  
   // Otherwise, we are computing the pressure.
   else
     return _p_star + (2 * _mu * _lambda) / (r * r) * (f_value + _K);
 }

Member Data Documentation

◆ _alpha_radians

const Real WedgeFunction::_alpha_radians

protected

The half-angle of the wedge, stored in radians.

Definition at line 39 of file WedgeFunction.h.

Referenced by value().

◆ _f

const Function& WedgeFunction::_f

protected

The pre-computed semi-analytic exact solution f(theta) as a PiecewiseLinear function.

Definition at line 88 of file WedgeFunction.h.

Referenced by value().

◆ _K

const Real WedgeFunction::_K

protected

The constant K from the Jeffery-Hamel solution, defined by: K = -f - 1/(4 * alpha^2) * (alpha * Re * f^2 + f'') which is required for computing the exact pressure:

p(r,theta) = p_star + (2 * mu * lambda) / (r^2) * (f(theta) + K)

Definition at line 66 of file WedgeFunction.h.

Referenced by value().

◆ _lambda

const Real WedgeFunction::_lambda

protected

The quantity u_max(r) * r, which is constant for this problem, and can be computed given the Reynolds number, nu, and alpha according to: lambda = _Re * _nu / _alpha_radians.

Definition at line 74 of file WedgeFunction.h.

Referenced by value().

◆ _mu

const Real WedgeFunction::_mu

protected

The (constant) dynamic viscosity of the fluid. Usually specified in [GlobalParams].

Definition at line 51 of file WedgeFunction.h.

Referenced by value().

◆ _nu

const Real WedgeFunction::_nu

protected

The kinematic viscosity = mu/rho.

Definition at line 57 of file WedgeFunction.h.

◆ _p_star

const Real WedgeFunction::_p_star

protected

The pressure constant, whose value is determined from the pressure pin.

Here, we assume the pressure is pinned to 0 at (r,theta)=(1,0). This value would need to change if the pressure was pinned to some other value.

Definition at line 82 of file WedgeFunction.h.

Referenced by value().

◆ _Re

const Real WedgeFunction::_Re

protected

The Reynolds number, (u_max(r) * r * alpha) / nu.

Note: the quantity u_max(r) * r := lambda = const.

Definition at line 45 of file WedgeFunction.h.

◆ _rho

const Real WedgeFunction::_rho

protected

The (constant) density of the fluid. Usually specified in [GlobalParams].

Definition at line 54 of file WedgeFunction.h.

◆ _var_num

const unsigned int WedgeFunction::_var_num

protected

The variable (vel_x==0, vel_y==1, p==2) being computed by this instance of WedgeFunction.

Definition at line 48 of file WedgeFunction.h.

Referenced by value().

The documentation for this class was generated from the following files:

navier_stokes/include/tests/WedgeFunction.h
navier_stokes/src/tests/WedgeFunction.C

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ WedgeFunction()

Member Function Documentation

◆ value()

Member Data Documentation

◆ _alpha_radians

◆ _f

◆ _K

◆ _lambda

◆ _mu

◆ _nu

◆ _p_star

◆ _Re

◆ _rho

◆ _var_num