refineable_axisym_advection_diffusion_elements.cc
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27 
28 namespace oomph
29 {
30  //==========================================================================
31  /// Add the element's contribution to the elemental residual vector
32  /// and/or elemental jacobian matrix.
33  /// This function overloads the standard version so that the possible
34  /// presence of hanging nodes is taken into account.
35  //=========================================================================
38  Vector<double>& residuals,
39  DenseMatrix<double>& jacobian,
40  DenseMatrix<double>& mass_matrix,
41  unsigned flag)
42  {
43  // Find out how many nodes there are in the element
44  const unsigned n_node = nnode();
45 
46  // Get the nodal index at which the unknown is stored
47  const unsigned u_nodal_index = this->u_index_axi_adv_diff();
48 
49  // Set up memory for the shape and test functions
50  Shape psi(n_node), test(n_node);
51  DShape dpsidx(n_node, 2), dtestdx(n_node, 2);
52 
53  // Set the value of n_intpt
54  const unsigned n_intpt = integral_pt()->nweight();
55 
56  // Set the Vector to hold local coordinates
57  Vector<double> s(2);
58 
59  // Get Peclet number
60  const double scaled_peclet = this->pe();
61 
62  // Get the Peclet number multiplied by the Strouhal number
63  const double scaled_peclet_st = this->pe_st();
64 
65  // Integers used to store the local equation number and local unknown
66  // indices for the residuals and jacobians
67  int local_eqn = 0, local_unknown = 0;
68 
69  // Local storage for pointers to hang_info objects
70  HangInfo *hang_info_pt = 0, *hang_info2_pt = 0;
71 
72  // Local variable to determine the ALE stuff
73  bool ALE_is_disabled_flag = this->ALE_is_disabled;
74 
75  // Loop over the integration points
76  for (unsigned ipt = 0; ipt < n_intpt; ipt++)
77  {
78  // Assign values of s
79  for (unsigned i = 0; i < 2; i++) s[i] = integral_pt()->knot(ipt, i);
80 
81  // Get the integral weight
82  double w = integral_pt()->weight(ipt);
83 
84  // Call the derivatives of the shape and test functions
86  ipt, psi, dpsidx, test, dtestdx);
87 
88  // Premultiply the weights and the Jacobian
89  double W = w * J;
90 
91  // Calculate local values of the function, initialise to zero
92  double dudt = 0.0;
93  double interpolated_u = 0.0;
94 
95  // These need to be a Vector to be ANSI C++, initialise to zero
97  Vector<double> interpolated_dudx(2, 0.0);
98  Vector<double> mesh_velocity(2, 0.0);
99 
100  // Calculate function value and derivatives:
101  //-----------------------------------------
102 
103  // Loop over nodes
104  for (unsigned l = 0; l < n_node; l++)
105  {
106  // Get the value at the node
107  double u_value = this->nodal_value(l, u_nodal_index);
108  interpolated_u += u_value * psi(l);
109  dudt += this->du_dt_axi_adv_diff(l) * psi(l);
110  // Loop over directions
111  for (unsigned j = 0; j < 2; j++)
112  {
113  interpolated_x[j] += nodal_position(l, j) * psi(l);
114  interpolated_dudx[j] += u_value * dpsidx(l, j);
115  }
116  }
117 
118  // Get the mesh velocity, if required
119  if (!ALE_is_disabled_flag)
120  {
121  for (unsigned l = 0; l < n_node; l++)
122  {
123  // Loop over directions
124  for (unsigned j = 0; j < 2; j++)
125  {
126  mesh_velocity[j] += dnodal_position_dt(l, j) * psi(l);
127  }
128  }
129  }
130 
131 
132  // Get body force
133  double source;
134  this->get_source_axi_adv_diff(ipt, interpolated_x, source);
135 
136 
137  // Get wind
138  //--------
139  Vector<double> wind(3);
140  this->get_wind_axi_adv_diff(ipt, s, interpolated_x, wind);
141 
142  // r is the first position component
143  double r = interpolated_x[0];
144 
145  // Assemble residuals and Jacobian
146  //================================
147 
148  // Loop over the nodes for the test functions
149  for (unsigned l = 0; l < n_node; l++)
150  {
151  // Local variables to store the number of master nodes and
152  // the weight associated with the shape function if the node is hanging
153  unsigned n_master = 1;
154  double hang_weight = 1.0;
155  // Local bool (is the node hanging)
156  bool is_node_hanging = this->node_pt(l)->is_hanging();
157 
158  // If the node is hanging, get the number of master nodes
159  if (is_node_hanging)
160  {
161  hang_info_pt = this->node_pt(l)->hanging_pt();
162  n_master = hang_info_pt->nmaster();
163  }
164  // Otherwise there is just one master node, the node itself
165  else
166  {
167  n_master = 1;
168  }
169 
170  // Loop over the number of master nodes
171  for (unsigned m = 0; m < n_master; m++)
172  {
173  // Get the local equation number and hang_weight
174  // If the node is hanging
175  if (is_node_hanging)
176  {
177  // Read out the local equation from the master node
178  local_eqn = this->local_hang_eqn(hang_info_pt->master_node_pt(m),
179  u_nodal_index);
180  // Read out the weight from the master node
181  hang_weight = hang_info_pt->master_weight(m);
182  }
183  // If the node is not hanging
184  else
185  {
186  // The local equation number comes from the node itself
187  local_eqn = this->nodal_local_eqn(l, u_nodal_index);
188  // The hang weight is one
189  hang_weight = 1.0;
190  }
191 
192  // If the nodal equation is not a boundary conditino
193  if (local_eqn >= 0)
194  {
195  // Add du/dt and body force/source term here
196  residuals[local_eqn] -= (scaled_peclet_st * dudt + source) * r *
197  test(l) * W * hang_weight;
198 
199  // The Advection Diffusion bit itself
200  residuals[local_eqn] -=
201  // radial terms
202  (interpolated_dudx[0] *
203  (scaled_peclet * wind[0] * test(l) + dtestdx(l, 0)) +
204  // azimuthal terms
205  (interpolated_dudx[1] *
206  (scaled_peclet * wind[1] * test(l) + dtestdx(l, 1)))) *
207  r * W * hang_weight;
208 
209  // ALE terms
210  if (!ALE_is_disabled)
211  {
212  residuals[local_eqn] +=
213  scaled_peclet_st *
214  (mesh_velocity[0] * interpolated_dudx[0] +
215  mesh_velocity[1] * interpolated_dudx[1]) *
216  test(l) * r * W * hang_weight;
217  }
218 
219 
220  // Calculate the Jacobian
221  if (flag)
222  {
223  // Local variables to store the number of master nodes
224  // and the weights associated with each hanging node
225  unsigned n_master2 = 1;
226  double hang_weight2 = 1.0;
227  // Loop over the nodes for the variables
228  for (unsigned l2 = 0; l2 < n_node; l2++)
229  {
230  // Local bool (is the node hanging)
231  bool is_node2_hanging = this->node_pt(l2)->is_hanging();
232  // If the node is hanging, get the number of master nodes
233  if (is_node2_hanging)
234  {
235  hang_info2_pt = this->node_pt(l2)->hanging_pt();
236  n_master2 = hang_info2_pt->nmaster();
237  }
238  // Otherwise there is one master node, the node itself
239  else
240  {
241  n_master2 = 1;
242  }
243 
244  // Loop over the master nodes
245  for (unsigned m2 = 0; m2 < n_master2; m2++)
246  {
247  // Get the local unknown and weight
248  // If the node is hanging
249  if (is_node2_hanging)
250  {
251  // Read out the local unknown from the master node
252  local_unknown = this->local_hang_eqn(
253  hang_info2_pt->master_node_pt(m2), u_nodal_index);
254  // Read out the hanging weight from the master node
255  hang_weight2 = hang_info2_pt->master_weight(m2);
256  }
257  // If the node is not hanging
258  else
259  {
260  // The local unknown number comes from the node
261  local_unknown = this->nodal_local_eqn(l2, u_nodal_index);
262  // The hang weight is one
263  hang_weight2 = 1.0;
264  }
265 
266  // If the unknown is not pinned
267  if (local_unknown >= 0)
268  {
269  // Add contribution to Elemental Matrix
270  // Mass matrix du/dt term
271  jacobian(local_eqn, local_unknown) -=
272  scaled_peclet_st * test(l) * psi(l2) *
273  this->node_pt(l2)->time_stepper_pt()->weight(1, 0) * r *
274  W * hang_weight * hang_weight2;
275 
276  // Add contribution to mass matrix
277  if (flag == 2)
278  {
279  mass_matrix(local_eqn, local_unknown) +=
280  scaled_peclet_st * test(l) * psi(l2) * r * W *
281  hang_weight * hang_weight2;
282  }
283 
284  // Add contribution to Elemental Matrix
285  // Assemble Jacobian term
286  jacobian(local_eqn, local_unknown) -=
287  // radial terms
288  (dpsidx(l2, 0) *
289  (scaled_peclet * wind[0] * test(l) + dtestdx(l, 0)) +
290  // azimuthal terms
291  (dpsidx(l2, 1) *
292  (scaled_peclet * wind[1] * test(l) + dtestdx(l, 1)))) *
293  r * W * hang_weight * hang_weight2;
294 
295  if (!ALE_is_disabled)
296  {
297  jacobian(local_eqn, local_unknown) +=
298  scaled_peclet_st *
299  (mesh_velocity[0] * dpsidx(l2, 0) +
300  mesh_velocity[1] * dpsidx(l2, 1)) *
301  test(l) * r * W * hang_weight * hang_weight2;
302  }
303  }
304  } // End of loop over master nodes
305  } // End of loop over nodes
306  } // End of Jacobian calculation
307 
308  } // End of non-zero equation
309 
310  } // End of loop over the master nodes for residual
311  } // End of loop over nodes
312 
313  } // End of loop over integration points
314  }
315 
316 
317  //====================================================================
318  // Force build of templates
319  //====================================================================
323 
324 } // namespace oomph
static char t char * s
Definition: cfortran.h:568
cstr elem_len * i
Definition: cfortran.h:603
virtual void get_wind_axi_adv_diff(const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &wind) const
Get wind at (Eulerian) position x and/or local coordinate s. This function is virtual to allow overlo...
virtual unsigned u_index_axi_adv_diff() const
Broken assignment operator.
double du_dt_axi_adv_diff(const unsigned &n) const
du/dt at local node n. Uses suitably interpolated value for hanging nodes.
virtual double dshape_and_dtest_eulerian_at_knot_axi_adv_diff(const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0
Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of ...
bool ALE_is_disabled
Boolean flag to indicate whether AlE formulation is disable.
virtual void get_source_axi_adv_diff(const unsigned &ipt, const Vector< double > &x, double &source) const
Get source term at (Eulerian) position x. This function is virtual to allow overloading in multi-phys...
const double & pe_st() const
Peclet number multiplied by Strouhal number.
A Class for the derivatives of shape functions The class design is essentially the same as Shape,...
Definition: shape.h:278
TimeStepper *& time_stepper_pt()
Return the pointer to the timestepper.
Definition: nodes.h:238
Node *& node_pt(const unsigned &n)
Return a pointer to the local node n.
Definition: elements.h:2175
double nodal_value(const unsigned &n, const unsigned &i) const
Return the i-th value stored at local node n. Produces suitably interpolated values for hanging nodes...
Definition: elements.h:2593
virtual double interpolated_x(const Vector< double > &s, const unsigned &i) const
Return FE interpolated coordinate x[i] at local coordinate s.
Definition: elements.cc:3962
int nodal_local_eqn(const unsigned &n, const unsigned &i) const
Return the local equation number corresponding to the i-th value at the n-th local node.
Definition: elements.h:1432
unsigned nnode() const
Return the number of nodes.
Definition: elements.h:2210
Integral *const & integral_pt() const
Return the pointer to the integration scheme (const version)
Definition: elements.h:1963
double nodal_position(const unsigned &n, const unsigned &i) const
Return the i-th coordinate at local node n. If the node is hanging, the appropriate interpolation is ...
Definition: elements.h:2317
double dnodal_position_dt(const unsigned &n, const unsigned &i) const
Return the i-th component of nodal velocity: dx/dt at local node n.
Definition: elements.h:2333
Class that contains data for hanging nodes.
Definition: nodes.h:742
double const & master_weight(const unsigned &i) const
Return weight for dofs on i-th master node.
Definition: nodes.h:808
Node *const & master_node_pt(const unsigned &i) const
Return a pointer to the i-th master node.
Definition: nodes.h:791
unsigned nmaster() const
Return the number of master nodes.
Definition: nodes.h:785
virtual double knot(const unsigned &i, const unsigned &j) const =0
Return local coordinate s[j] of i-th integration point.
virtual unsigned nweight() const =0
Return the number of integration points of the scheme.
virtual double weight(const unsigned &i) const =0
Return weight of i-th integration point.
HangInfo *const & hanging_pt() const
Return pointer to hanging node data (this refers to the geometric hanging node status) (const version...
Definition: nodes.h:1228
bool is_hanging() const
Test whether the node is geometrically hanging.
Definition: nodes.h:1285
void fill_in_generic_residual_contribution_axi_adv_diff(Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag)
Add the element's contribution to the elemental residual vector and/or Jacobian matrix flag=1: comput...
int local_hang_eqn(Node *const &node_pt, const unsigned &i)
Access function that returns the local equation number for the hanging node variables (values stored ...
Refineable version of QAxisymAdvectionDiffusionElement. Inherit from the standard QAxisymAdvectionDif...
A Class for shape functions. In simple cases, the shape functions have only one index that can be tho...
Definition: shape.h:76
virtual double weight(const unsigned &i, const unsigned &j) const
Access function for j-th weight for the i-th derivative.
Definition: timesteppers.h:594
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