GRINS-0.8.0
elastic_membrane_rayleigh_damping.C
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1 //-----------------------------------------------------------------------bl-
2 //--------------------------------------------------------------------------
3 //
4 // GRINS - General Reacting Incompressible Navier-Stokes
5 //
6 // Copyright (C) 2014-2017 Paul T. Bauman, Roy H. Stogner
7 // Copyright (C) 2010-2013 The PECOS Development Team
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23 //-----------------------------------------------------------------------el-
24 
25 // This class
26 #include "grins/elastic_membrane_rayleigh_damping.h"
27 
28 // GRINS
29 #include "grins/physics_naming.h"
30 #include "grins/elasticity_tensor.h"
31 #include "grins/assembly_context.h"
32 
33 // libMesh
34 #include "libmesh/getpot.h"
35 #include "libmesh/quadrature.h"
36 
37 namespace GRINS
38 {
39  template<typename StressStrainLaw>
40  ElasticMembraneRayleighDamping<StressStrainLaw>::ElasticMembraneRayleighDamping( const PhysicsName& physics_name,
41  const GetPot& input,
42  bool is_compressible )
43  : ElasticMembraneBase<StressStrainLaw>(physics_name,input,is_compressible),
44  _lambda_factor(input("Physics/"+PhysicsNaming::elastic_membrane_rayleigh_damping()+"/lambda_factor",0.0)),
45  _mu_factor(input("Physics/"+PhysicsNaming::elastic_membrane_rayleigh_damping()+"/mu_factor",0.0))
46  {
47  if( !input.have_variable("Physics/"+PhysicsNaming::elastic_membrane_rayleigh_damping()+"/lambda_factor") )
48  libmesh_error_msg("ERROR: Couldn't find Physics/"+PhysicsNaming::elastic_membrane_rayleigh_damping()+"/lambda_factor in input!");
49 
50  if( !input.have_variable("Physics/"+PhysicsNaming::elastic_membrane_rayleigh_damping()+"/mu_factor") )
51  libmesh_error_msg("ERROR: Couldn't find Physics/"+PhysicsNaming::elastic_membrane_rayleigh_damping()+"/mu_factor in input!");
52 
53  // If the user specified enabled subdomains in this Physics section,
54  // that's an error; we're slave to ElasticMembrane.
55  if( input.have_variable("Physics/"+PhysicsNaming::elastic_membrane_rayleigh_damping()+"/enabled_subdomains" ) )
56  libmesh_error_msg("ERROR: Cannot specify subdomains for "
57  +PhysicsNaming::elastic_membrane_rayleigh_damping()
58  +"! Must specify subdomains through "
59  +PhysicsNaming::elastic_membrane()+".");
60 
61  this->parse_enabled_subdomains(input,PhysicsNaming::elastic_membrane());
62  }
63 
64  template<typename StressStrainLaw>
65  void ElasticMembraneRayleighDamping<StressStrainLaw>::damping_residual
66  ( bool compute_jacobian, AssemblyContext & context )
67  {
68  // First do the mass part
69  this->mass_residual_impl(compute_jacobian,
70  context,
71  &libMesh::FEMContext::interior_rate,
72  &libMesh::DiffContext::get_elem_solution_rate_derivative,
73  _mu_factor);
74 
75  // Now do the stiffness part
76  const unsigned int n_u_dofs = context.get_dof_indices(this->_disp_vars.u()).size();
77 
78  const std::vector<libMesh::Real> &JxW =
79  this->get_fe(context)->get_JxW();
80 
81  // Residuals that we're populating
82  libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_disp_vars.u());
83  libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_disp_vars.v());
84  libMesh::DenseSubVector<libMesh::Number>* Fw = NULL;
85 
86  libMesh::DenseSubMatrix<libMesh::Number>& Kuu = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.u());
87  libMesh::DenseSubMatrix<libMesh::Number>& Kuv = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.v());
88 
89  libMesh::DenseSubMatrix<libMesh::Number>& Kvu = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.u());
90  libMesh::DenseSubMatrix<libMesh::Number>& Kvv = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.v());
91 
92  libMesh::DenseSubMatrix<libMesh::Number>* Kuw = NULL;
93  libMesh::DenseSubMatrix<libMesh::Number>* Kvw = NULL;
94 
95  libMesh::DenseSubMatrix<libMesh::Number>* Kwu = NULL;
96  libMesh::DenseSubMatrix<libMesh::Number>* Kwv = NULL;
97  libMesh::DenseSubMatrix<libMesh::Number>* Kww = NULL;
98 
99  if( this->_disp_vars.dim() == 3 )
100  {
101  Fw = &context.get_elem_residual(this->_disp_vars.w());
102 
103  Kuw = &context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.w());
104  Kvw = &context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.w());
105  Kwu = &context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.u());
106  Kwv = &context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.v());
107  Kww = &context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.w());
108  }
109 
110  unsigned int n_qpoints = context.get_element_qrule().n_points();
111 
112  // All shape function gradients are w.r.t. master element coordinates
113  const std::vector<std::vector<libMesh::Real> >& dphi_dxi =
114  this->get_fe(context)->get_dphidxi();
115 
116  const std::vector<std::vector<libMesh::Real> >& dphi_deta =
117  this->get_fe(context)->get_dphideta();
118 
119  const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( this->_disp_vars.u() );
120  const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( this->_disp_vars.v() );
121  const libMesh::DenseSubVector<libMesh::Number>* w_coeffs = NULL;
122 
123  const libMesh::DenseSubVector<libMesh::Number>& dudt_coeffs = context.get_elem_solution_rate( this->_disp_vars.u() );
124  const libMesh::DenseSubVector<libMesh::Number>& dvdt_coeffs = context.get_elem_solution_rate( this->_disp_vars.v() );
125  const libMesh::DenseSubVector<libMesh::Number>* dwdt_coeffs = NULL;
126 
127  if( this->_disp_vars.dim() == 3 )
128  {
129  w_coeffs = &context.get_elem_solution( this->_disp_vars.w() );
130  dwdt_coeffs = &context.get_elem_solution_rate( this->_disp_vars.w() );
131  }
132 
133  // Need these to build up the covariant and contravariant metric tensors
134  const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi();
135  const std::vector<libMesh::RealGradient>& dxdeta = this->get_fe(context)->get_dxyzdeta();
136 
137  for (unsigned int qp=0; qp != n_qpoints; qp++)
138  {
139  // Gradients are w.r.t. master element coordinates
140  libMesh::Gradient grad_u, grad_v, grad_w;
141  libMesh::Gradient dgradu_dt, dgradv_dt, dgradw_dt;
142 
143  for( unsigned int d = 0; d < n_u_dofs; d++ )
144  {
145  libMesh::RealGradient u_gradphi( dphi_dxi[d][qp], dphi_deta[d][qp] );
146  grad_u += u_coeffs(d)*u_gradphi;
147  grad_v += v_coeffs(d)*u_gradphi;
148 
149  dgradu_dt += dudt_coeffs(d)*u_gradphi;
150  dgradv_dt += dvdt_coeffs(d)*u_gradphi;
151 
152  if( this->_disp_vars.dim() == 3 )
153  {
154  grad_w += (*w_coeffs)(d)*u_gradphi;
155  dgradw_dt += (*dwdt_coeffs)(d)*u_gradphi;
156  }
157  }
158 
159  libMesh::RealGradient grad_x( dxdxi[qp](0), dxdeta[qp](0) );
160  libMesh::RealGradient grad_y( dxdxi[qp](1), dxdeta[qp](1) );
161  libMesh::RealGradient grad_z( dxdxi[qp](2), dxdeta[qp](2) );
162 
163 
164  libMesh::TensorValue<libMesh::Real> a_cov, a_contra, A_cov, A_contra;
165  libMesh::Real lambda_sq = 0;
166 
167  this->compute_metric_tensors( qp, *(this->get_fe(context)), context,
168  grad_u, grad_v, grad_w,
169  a_cov, a_contra, A_cov, A_contra,
170  lambda_sq );
171 
172  const unsigned int manifold_dim = 2; // The manifold dimension is always 2 for this physics
173 
174  // Compute stress and elasticity tensors
175  libMesh::TensorValue<libMesh::Real> tau;
176  ElasticityTensor C;
177  this->_stress_strain_law.compute_stress_and_elasticity(manifold_dim,a_contra,a_cov,A_contra,A_cov,tau,C);
178 
179  libMesh::Real jac = JxW[qp];
180 
181  for (unsigned int i=0; i != n_u_dofs; i++)
182  {
183  libMesh::RealGradient u_gradphi( dphi_dxi[i][qp], dphi_deta[i][qp] );
184 
185  for( unsigned int alpha = 0; alpha < manifold_dim; alpha++ )
186  {
187  for( unsigned int beta = 0; beta < manifold_dim; beta++ )
188  {
189  const libMesh::Real common_factor = _lambda_factor*0.5*this->_h0*jac;
190  const libMesh::Real factor = common_factor*tau(alpha,beta);
191 
192  libMesh::Real u_diagterm = dgradu_dt(beta)*u_gradphi(alpha) + dgradu_dt(alpha)*u_gradphi(beta);
193  libMesh::Real v_diagterm = dgradv_dt(beta)*u_gradphi(alpha) + dgradv_dt(alpha)*u_gradphi(beta);
194  libMesh::Real w_diagterm = dgradw_dt(beta)*u_gradphi(alpha) + dgradw_dt(alpha)*u_gradphi(beta);
195 
196  Fu(i) += factor*u_diagterm;
197  Fv(i) += factor*v_diagterm;
198 
199  if( this->_disp_vars.dim() == 3 )
200  (*Fw)(i) += factor*w_diagterm;
201 
202  for( unsigned int lambda = 0; lambda < manifold_dim; lambda++ )
203  {
204  for( unsigned int mu = 0; mu < manifold_dim; mu++ )
205  {
206  const libMesh::Real C1 = common_factor*C(alpha,beta,lambda,mu);
207 
208  const libMesh::Real gamma_u = 0.5*( dgradu_dt(lambda)*(grad_x(mu)+grad_u(mu)) +
209  (grad_x(lambda)+grad_u(lambda))*dgradu_dt(mu) );
210 
211  const libMesh::Real gamma_v = 0.5*( dgradv_dt(lambda)*(grad_y(mu)+grad_v(mu)) +
212  (grad_y(lambda)+grad_v(lambda))*dgradv_dt(mu) );
213 
214  const libMesh::Real x_term = C1*( (grad_x(beta)+grad_u(beta))*u_gradphi(alpha) +
215  (grad_x(alpha)+grad_u(alpha))*u_gradphi(beta) );
216 
217  const libMesh::Real y_term = C1*( (grad_y(beta)+grad_v(beta))*u_gradphi(alpha) +
218  (grad_y(alpha)+grad_v(alpha))*u_gradphi(beta) );
219 
220  libMesh::Real gamma_sum = gamma_u + gamma_v;
221  if( this->_disp_vars.dim() == 3 )
222  {
223  const libMesh::Real gamma_w = 0.5*( dgradw_dt(lambda)*(grad_z(mu)+grad_w(mu)) +
224  (grad_z(lambda)+grad_w(lambda))*dgradw_dt(mu) );
225  gamma_sum += gamma_w;
226  }
227 
228  Fu(i) += x_term*gamma_sum;
229 
230  Fv(i) += y_term*gamma_sum;
231 
232  if( this->_disp_vars.dim() == 3 )
233  {
234  const libMesh::Real z_term = C1*( (grad_z(beta)+grad_w(beta))*u_gradphi(alpha) +
235  (grad_z(alpha)+grad_w(alpha))*u_gradphi(beta) );
236 
237  (*Fw)(i) += z_term*gamma_sum;
238  }
239  }
240  }
241  }
242  }
243  }
244 
245  if( compute_jacobian )
246  {
247  for (unsigned int i=0; i != n_u_dofs; i++)
248  {
249  libMesh::RealGradient u_gradphi_i( dphi_dxi[i][qp], dphi_deta[i][qp] );
250 
251  for (unsigned int j=0; j != n_u_dofs; j++)
252  {
253  libMesh::RealGradient u_gradphi_j( dphi_dxi[j][qp], dphi_deta[j][qp] );
254 
255  for( unsigned int alpha = 0; alpha < manifold_dim; alpha++ )
256  {
257  for( unsigned int beta = 0; beta < manifold_dim; beta++ )
258  {
259  const libMesh::Real common_factor = _lambda_factor*0.5*this->_h0*jac;
260 
261  const libMesh::Real factor = common_factor*tau(alpha,beta);
262 
263  const libMesh::Real ddiagterm = u_gradphi_j(beta)*u_gradphi_i(alpha) + u_gradphi_j(alpha)*u_gradphi_i(beta);
264 
265  Kuu(i,j) += factor*ddiagterm*context.get_elem_solution_rate_derivative();
266  Kvv(i,j) += factor*ddiagterm*context.get_elem_solution_rate_derivative();
267 
268  if( this->_disp_vars.dim() == 3 )
269  (*Kww)(i,j) += factor*ddiagterm*context.get_elem_solution_rate_derivative();
270 
271  libMesh::Real u_diagterm = dgradu_dt(beta)*u_gradphi_i(alpha) + dgradu_dt(alpha)*u_gradphi_i(beta);
272  libMesh::Real v_diagterm = dgradv_dt(beta)*u_gradphi_i(alpha) + dgradv_dt(alpha)*u_gradphi_i(beta);
273  libMesh::Real w_diagterm = 0.0;
274  if( this->_disp_vars.dim() == 3 )
275  w_diagterm = dgradw_dt(beta)*u_gradphi_i(alpha) + dgradw_dt(alpha)*u_gradphi_i(beta);
276 
277  for( unsigned int lambda = 0; lambda < manifold_dim; lambda++ )
278  {
279  for( unsigned int mu = 0; mu < manifold_dim; mu++ )
280  {
281  const libMesh::Real dgamma_du = 0.5*( u_gradphi_j(lambda)*(grad_x(mu)+grad_u(mu)) +
282  (grad_x(lambda)+grad_u(lambda))*u_gradphi_j(mu) );
283 
284  const libMesh::Real dgamma_dv = 0.5*( u_gradphi_j(lambda)*(grad_y(mu)+grad_v(mu)) +
285  (grad_y(lambda)+grad_v(lambda))*u_gradphi_j(mu) );
286 
287  const libMesh::Real C1 = common_factor*C(alpha,beta,lambda,mu);
288 
289  const libMesh::Real dfactor_du = C1*dgamma_du*context.get_elem_solution_derivative();
290  const libMesh::Real dfactor_dv = C1*dgamma_dv*context.get_elem_solution_derivative();
291 
292  Kuu(i,j) += u_diagterm*dfactor_du;
293  Kuv(i,j) += u_diagterm*dfactor_dv;
294 
295  Kvu(i,j) += v_diagterm*dfactor_du;
296  Kvv(i,j) += v_diagterm*dfactor_dv;
297 
298  if( this->_disp_vars.dim() == 3 )
299  {
300  const libMesh::Real dgamma_dw = 0.5*( u_gradphi_j(lambda)*(grad_z(mu)+grad_w(mu)) +
301  (grad_z(lambda)+grad_w(lambda))*u_gradphi_j(mu) );
302 
303  const libMesh::Real dfactor_dw = C1*dgamma_dw*context.get_elem_solution_derivative();
304 
305  (*Kuw)(i,j) += u_diagterm*dfactor_dw;
306 
307  (*Kvw)(i,j) += v_diagterm*dfactor_dw;
308 
309  (*Kwu)(i,j) += w_diagterm*dfactor_du;
310  (*Kwv)(i,j) += w_diagterm*dfactor_dv;
311  (*Kww)(i,j) += w_diagterm*dfactor_dw;
312  }
313 
314  const libMesh::Real gamma_u = 0.5*( dgradu_dt(lambda)*(grad_x(mu)+grad_u(mu)) +
315  (grad_x(lambda)+grad_u(lambda))*dgradu_dt(mu) );
316 
317  const libMesh::Real gamma_v = 0.5*( dgradv_dt(lambda)*(grad_y(mu)+grad_v(mu)) +
318  (grad_y(lambda)+grad_v(lambda))*dgradv_dt(mu) );
319 
320  const libMesh::Real x_term = C1*( (grad_x(beta)+grad_u(beta))*u_gradphi_i(alpha) +
321  (grad_x(alpha)+grad_u(alpha))*u_gradphi_i(beta) );
322 
323  const libMesh::Real y_term = C1*( (grad_y(beta)+grad_v(beta))*u_gradphi_i(alpha) +
324  (grad_y(alpha)+grad_v(alpha))*u_gradphi_i(beta) );
325 
326  libMesh::Real gamma_sum = gamma_u + gamma_v;
327  if( this->_disp_vars.dim() == 3 )
328  {
329  const libMesh::Real gamma_w = 0.5*( dgradw_dt(lambda)*(grad_z(mu)+grad_w(mu)) +
330  (grad_z(lambda)+grad_w(lambda))*dgradw_dt(mu) );
331  gamma_sum += gamma_w;
332  }
333 
334  // Here, we're missing derivatives of C(alpha,beta,lambda,mu) w.r.t. strain
335  // Nonzero for hyperelasticity models
336  const libMesh::Real dxterm_du = C1*( u_gradphi_j(beta)*u_gradphi_i(alpha)
337  + u_gradphi_j(alpha)*u_gradphi_i(beta) )*context.get_elem_solution_derivative();
338 
339  const libMesh::Real dyterm_dv = dxterm_du;
340 
341  Kuu(i,j) += gamma_sum*dxterm_du;
342 
343  Kvv(i,j) += gamma_sum*dyterm_dv;
344 
345  libMesh::Real z_term = 0.0;
346 
347  if( this->_disp_vars.dim() == 3 )
348  {
349  z_term = C1*( (grad_z(beta)+grad_w(beta))*u_gradphi_i(alpha) +
350  (grad_z(alpha)+grad_w(alpha))*u_gradphi_i(beta) );
351 
352  // Here, we're missing derivatives of C(alpha,beta,lambda,mu) w.r.t. strain
353  // Nonzero for hyperelasticity models
354  const libMesh::Real dzterm_dw = dxterm_du;
355 
356  (*Kww)(i,j) += gamma_sum*dzterm_dw;
357  }
358 
359  const libMesh::Real dgamma_sum_du = 0.5*( u_gradphi_j(lambda)*(grad_x(mu)+grad_u(mu))*context.get_elem_solution_rate_derivative()
360  + dgradu_dt(lambda)*u_gradphi_j(mu)*context.get_elem_solution_derivative()
361  + u_gradphi_j(mu)*(grad_x(lambda)+grad_u(lambda))*context.get_elem_solution_rate_derivative()
362  + dgradu_dt(mu)*u_gradphi_j(lambda)*context.get_elem_solution_derivative() );
363 
364  const libMesh::Real dgamma_sum_dv = 0.5*( u_gradphi_j(lambda)*(grad_y(mu)+grad_v(mu))*context.get_elem_solution_rate_derivative()
365  + dgradv_dt(lambda)*u_gradphi_j(mu)*context.get_elem_solution_derivative()
366  + u_gradphi_j(mu)*(grad_y(lambda)+grad_v(lambda))*context.get_elem_solution_rate_derivative()
367  + dgradv_dt(mu)*u_gradphi_j(lambda)*context.get_elem_solution_derivative() );
368 
369  Kuu(i,j) += x_term*dgamma_sum_du;
370  Kuv(i,j) += x_term*dgamma_sum_dv;
371 
372  Kvu(i,j) += y_term*dgamma_sum_du;
373  Kvv(i,j) += y_term*dgamma_sum_dv;
374 
375  if( this->_disp_vars.dim() == 3 )
376  {
377  const libMesh::Real dgamma_sum_dw = 0.5*( u_gradphi_j(lambda)*(grad_z(mu)+grad_w(mu))*context.get_elem_solution_rate_derivative()
378  + dgradw_dt(lambda)*u_gradphi_j(mu)*context.get_elem_solution_derivative()
379  + u_gradphi_j(mu)*(grad_z(lambda)+grad_w(lambda))*context.get_elem_solution_rate_derivative()
380  + dgradw_dt(mu)*u_gradphi_j(lambda)*context.get_elem_solution_derivative() );
381 
382  (*Kuw)(i,j) += x_term*dgamma_sum_dw;
383  (*Kvw)(i,j) += y_term*dgamma_sum_dw;
384  (*Kwu)(i,j) += z_term*dgamma_sum_du;
385  (*Kwv)(i,j) += z_term*dgamma_sum_dv;
386  (*Kww)(i,j) += z_term*dgamma_sum_dw;
387  }
388  }
389  }
390  }
391  }
392  }
393  }
394  }
395 
396  }
397  }
398 
399 
400 } // end namespace GRINS
assembly_context.h
elastic_membrane_rayleigh_damping.h
GRINS
GRINS namespace.
Definition: arrhenius_catalycity.h:31
GRINS::PhysicsNaming::elastic_membrane
static PhysicsName elastic_membrane()
Definition: physics_naming.h:167
physics_naming.h
elasticity_tensor.h
GRINS::PhysicsName
std::string PhysicsName
Definition: physics_naming.h:33
GRINS::ElasticMembraneRayleighDamping::damping_residual
virtual void damping_residual(bool compute_jacobian, AssemblyContext &context)
Time dependent part(s) of physics for element interiors.
Definition: elastic_membrane_rayleigh_damping.C:66
GRINS::Physics::parse_enabled_subdomains
void parse_enabled_subdomains(const GetPot &input, const std::string &physics_name)
Definition: physics.C:65
GRINS::PhysicsNaming::elastic_membrane_rayleigh_damping
static PhysicsName elastic_membrane_rayleigh_damping()
Definition: physics_naming.h:176
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