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axisymmetric_mesh1d.hpp
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/*-------------------------------------------------------
Copyright (c) 2014,2015 Fabien Georget <fabieng@princeton.edu>, Princeton University
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of the Princeton University nor the
names of its contributors may be used to endorse or promote products
derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
---------------------------------------------------------*/
#ifndef SPECMICP_DFPM_MESHES_AXISYMMETRICMESH1D_HPP
#define SPECMICP_DFPM_MESHES_AXISYMMETRICMESH1D_HPP
#include "mesh1d.hpp"
namespace specmicp {
namespace mesh {
//! \brief A generic Axisymmetric 1D mesh
class AxisymmetricMesh1D: public Mesh1D
{
public:
const index_t radius = 0;
const index_t cell_vol_0 = 1;
const index_t cell_vol_1 = 2;
//! \brief Build an axisymmetric 1D mesh
//!
//! \param radius is a vector of the position of the nodes
//! \param height is the height of the sample (or depth)
AxisymmetricMesh1D(Vector radius, scalar_t height):
Mesh1D(radius.rows()),
m_height(height),
m_data(radius.rows(), 3),
m_face_radius(radius.rows()-1)
{
// radius
m_data.col(0) = radius;
// Radius of the faces
for (index_t element=0; element<nb_elements(); ++element)
{
m_face_radius(element) = (radius(element+1)+radius(element))/2.0;
}
// Volume at the left of the cell
m_data(0, cell_vol_0) = 0.0;
for (index_t node=1; node<nb_nodes(); ++node)
{
m_data(node, cell_vol_0) = M_PI*height*(std::pow(m_face_radius(node-1), 2)
- std::pow(radius(node), 2));
}
// Volume of the cell at the right of the node
for (index_t node=0; node<nb_nodes()-1; ++node)
{
m_data(node, cell_vol_1) = M_PI*height*(std::pow(radius(node), 2)
- std::pow(m_face_radius(node), 2));
}
m_data(nb_nodes()-1, cell_vol_1) = 0.0;
}
//! \brief Return the radius of an element
scalar_t get_radius(index_t element, index_t enode) {
return m_data(get_node(element, enode), radius);
}
//! \brief Return the radius of the face
scalar_t get_radius_face(index_t element) {
return m_face_radius(element);
}
//! \brief Return the position (meaning may vary with the mesh) of the node
scalar_t get_position(index_t node) {return m_data(node, radius);}
//! \brief Return the length of an element
scalar_t get_dx(index_t element) {
return get_radius(element, 0) - get_radius(element, 1);}
//! \brief Return the area of the face at the middle of an element
scalar_t get_face_area(index_t element) {
return 2*M_PI*m_face_radius(element)*m_height;}
//! \brief Return the volume of an element
scalar_t get_volume_element(index_t element) {
return (m_data(get_node(element, 0), cell_vol_1)
+ m_data(get_node(element, 1), cell_vol_0));}
//! \brief Return the volume of a cell (element of the dual mesh)
scalar_t get_volume_cell(index_t node) {
return (m_data(node, cell_vol_0) + m_data(node, cell_vol_1));}
//! \brief Return the volume of a cell inside an element
virtual scalar_t get_volume_cell_element(index_t element, index_t enode) {
if (enode == 0)
return m_data(get_node(element, enode), cell_vol_1);
else
return m_data(get_node(element, enode), cell_vol_0);
}
private:
scalar_t m_height;
Matrix m_data;
Vector m_face_radius;
};
//! \brief Return a shared_ptr to an axisymmetric mesh
//!
//! \param radius is a vector of the position of the nodes
//! \param height is the height of the sample (or depth)
inline Mesh1DPtr axisymmetric_mesh1d(Vector radius, scalar_t height)
{
return std::static_pointer_cast<Mesh1D>(
std::make_shared<AxisymmetricMesh1D>(radius, height));
}
//! \brief Factory method to build a pointer to a uniform axisymmetric 1D mesh
//!
//! \param nb_nodes number of nodes in the mesh
//! \param radius of the first node (biggest radius in the mesh)
//! \param dx length of an element
//! \param height is the height of the sample (or depth)
//!
//! Note: this method buil an AxisymmetricMesh1D instance while
//! the specmicp::mesh::axisymmetric_uniform_mesh1d method build a
//! specmicp::mesh::AxisymmetricUniformMesh1D instance.
inline Mesh1DPtr uniform_axisymmetric_mesh1d(index_t nb_nodes, scalar_t radius, scalar_t dx, scalar_t height)
{
Vector radius_s(nb_nodes);
for (index_t node=0; node<nb_nodes; ++node)
{
radius_s(node) = radius - node*dx;
}
return std::static_pointer_cast<Mesh1D>(
std::make_shared<AxisymmetricMesh1D>(radius_s, height));
}
} // end namespace mesh
} // end namespace specmicp
#endif // SPECMICP_DFPM_MESHES_AXISYMMETRICMESH1D_HPP

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