supg_advection_diffusion_elements.cc
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27
28
29namespace oomph
30{
31 //======================================================================
32 /// QSUPGAdvectionDiffusionElement<DIM,NNODE_1D> elements are
33 /// SUPG-stabilised Advection Diffusion elements with
34 /// NNODE_1D nodal points in each coordinate direction. Inherits
35 /// from QAdvectionDiffusionElement and overwrites their
36 /// test functions
37 ///
38 //======================================================================
39
40 //======================================================================
41 /// Define the shape functions and test functions and derivatives
42 /// w.r.t. global coordinates and return Jacobian of mapping.
43 ///
44 /// SUPG stabilisation: Petrov-Galerkin, i.e. test functions \f$ \ne \f$
45 /// shape functions
46 //======================================================================
47 template<unsigned DIM, unsigned NNODE_1D>
50 Shape& psi,
51 DShape& dpsidx,
52 Shape& test,
53 DShape& dtestdx) const
54 {
55 // Call the geometrical shape functions and derivatives
56 double J = QElement<DIM, NNODE_1D>::dshape_eulerian(s, psi, dpsidx);
57
58 // Find out how many nodes there are
59 unsigned n_node = this->nnode();
60
61 // Calculate Eulerian coordinates
62 Vector<double> interpolated_x(DIM, 0.0);
63
64 // Loop over nodes
65 for (unsigned l = 0; l < n_node; l++)
66 {
67 // Loop over directions
68 for (unsigned j = 0; j < DIM; j++)
69 {
70 interpolated_x[j] += this->nodal_position(l, j) * psi[l];
71 }
72 }
73
74 // Get wind
75 Vector<double> wind(DIM);
76 // Dummy ipt argument
77 unsigned ipt = 0;
78 this->get_wind_adv_diff(ipt, s, interpolated_x, wind);
79
80 // Loop over the test functions and derivatives and set them equal to the
81 // shape functions + add stabilisation
82 for (unsigned j = 0; j < n_node; j++)
83 {
84 test[j] = psi[j];
85
86 for (unsigned i = 0; i < DIM; i++)
87 {
88 dtestdx(j, i) = dpsidx(j, i);
89 test[j] += Tau_SUPG * wind[i] * dpsidx(j, i);
90 }
91 }
92
93 // Return the jacobian
94 return J;
95 }
96
97
98 //======================================================================
99 /// Define the shape functions and test functions and derivatives
100 /// w.r.t. global coordinates and return Jacobian of mapping.
101 ///
102 /// SUPG stabilisation: Petrov-Galerkin, i.e. test functions \f$ \ne \f$
103 /// shape functions
104 //======================================================================
105 template<unsigned DIM, unsigned NNODE_1D>
108 Shape& psi,
109 DShape& dpsidx,
110 Shape& test,
111 DShape& dtestdx) const
112 {
113 // Call the geometrical shape functions and derivatives
114 double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
115
116 // Find out how many nodes there are
117 unsigned n_node = this->nnode();
118
119 // Calculate Eulerian coordinates
120 Vector<double> interpolated_x(DIM, 0.0);
121
122 // Loop over nodes
123 for (unsigned l = 0; l < n_node; l++)
124 {
125 // Loop over directions
126 for (unsigned j = 0; j < DIM; j++)
127 {
128 interpolated_x[j] += this->nodal_position(l, j) * psi(l);
129 }
130 }
131
132 // Find the dimension of the element
133 unsigned Dim = this->dim();
134 // Storage for the local coordinates of the integration point
136 // Set the local coordinate
137 for (unsigned i = 0; i < Dim; i++)
138 {
139 s[i] = this->integral_pt()->knot(ipt, i);
140 }
141
142 // Get wind
143 Vector<double> wind(DIM);
144 this->get_wind_adv_diff(ipt, s, interpolated_x, wind);
145
146 // Loop over the test functions and derivatives and set them equal to the
147 // shape functions + add stabilisation
148 for (unsigned j = 0; j < n_node; j++)
149 {
150 test(j) = psi(j);
151 for (unsigned i = 0; i < DIM; i++)
152 {
153 dtestdx(j, i) = dpsidx(j, i);
154 test(j) += Tau_SUPG * wind[i] * dpsidx(j, i);
155 }
156 }
157
158
159 // Return the jacobian
160 return J;
161 }
162
163
164 // Force template instantiation.
168
169
173
174
175 // Force template instantiation.
179
180
184
185
186} // namespace oomph
static char t char * s
Definition: cfortran.h:568
cstr elem_len * i
Definition: cfortran.h:603
A Class for the derivatives of shape functions The class design is essentially the same as Shape,...
Definition: shape.h:278
/////////////////////////////////////////////////////////////////////// /////////////////////////////...
Definition: Qelements.h:459
QSUPGAdvectionDiffusionElement<DIM,NNODE_1D> elements are SUPG-stabilised Advection Diffusion element...
double dshape_and_dtest_eulerian_adv_diff(const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
Shape, test functions & derivs. w.r.t. to global coords. Return Jacobian.
double dshape_and_dtest_eulerian_at_knot_adv_diff(const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
Shape, test functions & derivs. w.r.t. to global coords. Return Jacobian.
////////////////////////////////////////////////////////////////////// //////////////////////////////...
A Class for shape functions. In simple cases, the shape functions have only one index that can be tho...
Definition: shape.h:76
unsigned Dim
Dimension of zeta tuples (set by get_dim_helper) – needed because we store the scalar coordinates in ...
Definition: multi_domain.cc:60
//////////////////////////////////////////////////////////////////// ////////////////////////////////...