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// $Id: flow_function.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2007 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__flow_function_h
#define __deal2__flow_function_h
#include <deal.II/base/config.h>
#include <deal.II/base/function.h>
#include <deal.II/base/point.h>
#include <deal.II/base/thread_management.h>
DEAL_II_NAMESPACE_OPEN
namespace Functions
{
/**
* Base class for analytic solutions to incompressible flow problems.
*
* Additional to the Function interface, this function provides for an
* offset of the pressure: if the pressure of the computed solution
* has an integral mean value different from zero, this value can be
* given to pressure_adjustment() in order to compute correct pressure
* errors.
*
* @note Derived classes should implement pressures with integral mean
* value zero always.
*
* @note Thread safety: Some of the functions make use of internal data to compute
* values. Therefore, every thread should obtain its own object of
* derived classes.
*
* @ingroup functions
* @author Guido Kanschat, 2007
*/
template <int dim>
class FlowFunction : public Function<dim>
{
public:
/**
* Constructor, setting up some
* internal data structures.
*/
FlowFunction();
/**
* Virtual destructor.
*/
virtual ~FlowFunction();
/**
* Store an adjustment for the
* pressure function, such that
* its mean value is
* <tt>p</tt>.
*/
void pressure_adjustment(double p);
/**
* Values in a structure more
* suitable for vector valued
* functions. The outer vector
* is indexed by solution
* component, the inner by
* quadrature point.
*/
virtual void vector_values (const std::vector<Point<dim> > &points,
std::vector<std::vector<double> > &values) const = 0;
/**
* Gradients in a structure more
* suitable for vector valued
* functions. The outer vector
* is indexed by solution
* component, the inner by
* quadrature point.
*/
virtual void vector_gradients (const std::vector<Point<dim> > &points,
std::vector<std::vector<Tensor<1,dim> > > &gradients) const = 0;
/**
* Force terms in a structure more
* suitable for vector valued
* functions. The outer vector
* is indexed by solution
* component, the inner by
* quadrature point.
*
* @warning This is not the
* true Laplacian, but the
* force term to be used as
* right hand side in Stokes'
* equations
*/
virtual void vector_laplacians (const std::vector<Point<dim> > &points,
std::vector<std::vector<double> > &values) const = 0;
virtual void vector_value (const Point<dim> &points, Vector<double> &value) const;
virtual double value (const Point<dim> &points, const unsigned int component) const;
virtual void vector_value_list (const std::vector<Point<dim> > &points,
std::vector<Vector<double> > &values) const;
virtual void vector_gradient_list (const std::vector<Point<dim> > &points,
std::vector<std::vector<Tensor<1,dim> > > &gradients) const;
/**
* The force term in the
* momentum equation.
*/
virtual void vector_laplacian_list (const std::vector<Point<dim> > &points,
std::vector<Vector<double> > &values) const;
std::size_t memory_consumption () const;
protected:
/**
* Mean value of the pressure
* to be added by derived
* classes.
*/
double mean_pressure;
private:
/**
* A mutex that guards the
* following scratch arrays.
*/
mutable Threads::Mutex mutex;
/**
* Auxiliary values for the usual
* Function interface.
*/
mutable std::vector<std::vector<double> > aux_values;
/**
* Auxiliary values for the usual
* Function interface.
*/
mutable std::vector<std::vector<Tensor<1,dim> > > aux_gradients;
};
/**
* Laminar pipe flow in two and three dimensions. The channel
* stretches along the <i>x</i>-axis and has radius @p radius. The
* @p Reynolds number is used to scale the pressure properly for a
* Navier-Stokes problem.
*
* @ingroup functions
* @author Guido Kanschat, 2007
*/
template <int dim>
class PoisseuilleFlow : public FlowFunction<dim>
{
public:
/**
* Construct an object for the
* given channel radius
* <tt>r</tt> and the Reynolds
* number <tt>Re</tt>.
*/
PoisseuilleFlow<dim> (const double r,
const double Re);
virtual ~PoisseuilleFlow();
virtual void vector_values (const std::vector<Point<dim> > &points,
std::vector<std::vector<double> > &values) const;
virtual void vector_gradients (const std::vector<Point<dim> > &points,
std::vector<std::vector<Tensor<1,dim> > > &gradients) const;
virtual void vector_laplacians (const std::vector<Point<dim> > &points,
std::vector<std::vector<double> > &values) const;
private:
const double radius;
const double Reynolds;
};
/**
* Artificial divergence free function with homogeneous boundary
* conditions on the cube [-1,1]<sup>dim</sup>.
*
* The function in 2D is
* @f[
* \left(\begin{array}{c}u\\v\\p\end{array}\right)
* \left(\begin{array}{c}\cos^2x \sin y\cos y\\-\sin x\cos x\cos^2y\\
* \sin x\cos x\sin y\cos y\end{array}\right)
* @f]
* @ingroup functions
* @author Guido Kanschat, 2007
*/
template <int dim>
class StokesCosine :
public FlowFunction<dim>
{
public:
/**
* Constructor setting the
* Reynolds number required for
* pressure computation and
* scaling of the right hand side.
*/
StokesCosine (const double viscosity = 1., const double reaction = 0.);
/**
* Change the viscosity and the
* reaction parameter.
*/
void set_parameters (const double viscosity, const double reaction);
virtual ~StokesCosine();
virtual void vector_values (const std::vector<Point<dim> > &points,
std::vector<std::vector<double> > &values) const;
virtual void vector_gradients (const std::vector<Point<dim> > &points,
std::vector<std::vector<Tensor<1,dim> > > &gradients) const;
virtual void vector_laplacians (const std::vector<Point<dim> > &points,
std::vector<std::vector<double> > &values) const;
private:
/// The viscosity
double viscosity;
/// The reaction parameter
double reaction;
};
/**
* The solution to Stokes' equations on an L-shaped domain.
*
* Taken from Houston, Schötzau, Wihler, proceeding ENUMATH 2003.
*
* @ingroup functions
* @author Guido Kanschat, 2007
*/
class StokesLSingularity : public FlowFunction<2>
{
public:
/// Constructor setting upsome data.
StokesLSingularity();
virtual void vector_values (const std::vector<Point<2> > &points,
std::vector<std::vector<double> > &values) const;
virtual void vector_gradients (const std::vector<Point<2> > &points,
std::vector<std::vector<Tensor<1,2> > > &gradients) const;
virtual void vector_laplacians (const std::vector<Point<2> > &points,
std::vector<std::vector<double> > &values) const;
private:
/// The auxiliary function Psi.
double Psi(double phi) const;
/// The derivative of Psi()
double Psi_1(double phi) const;
/// The 2nd derivative of Psi()
double Psi_2(double phi) const;
/// The 3rd derivative of Psi()
double Psi_3(double phi) const;
/// The 4th derivative of Psi()
double Psi_4(double phi) const;
/// The angle of the reentrant corner
const double omega;
/// The exponent of the radius
static const double lambda;
/// Cosine of lambda times omega
const double coslo;
/// Auxiliary variable 1+lambda
const double lp;
/// Auxiliary variable 1-lambda
const double lm;
};
/**
* Flow solution in 2D by Kovasznay (1947).
*
* This function is valid on the half plane right of the line
* <i>x=1/2</i>.
*
* @ingroup functions
* @author Guido Kanschat, 2007
*/
class Kovasznay : public FlowFunction<2>
{
public:
/**
* Construct an object for the
* give Reynolds number
* <tt>Re</tt>. If the
* parameter <tt>Stokes</tt> is
* true, the right hand side of
* the momentum equation
* returned by
* vector_laplacians() contains
* the nonlinearity, such that
* the Kovasznay solution can
* be obtained as the solution
* to a Stokes problem.
*/
Kovasznay (const double Re, bool Stokes = false);
virtual ~Kovasznay();
virtual void vector_values (const std::vector<Point<2> > &points,
std::vector<std::vector<double> > &values) const;
virtual void vector_gradients (const std::vector<Point<2> > &points,
std::vector<std::vector<Tensor<1,2> > > &gradients) const;
virtual void vector_laplacians (const std::vector<Point<2> > &points,
std::vector<std::vector<double> > &values) const;
/// The value of lambda.
double lambda () const;
private:
const double Reynolds;
double lbda;
double p_average;
const bool stokes;
};
}
DEAL_II_NAMESPACE_CLOSE
#endif
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