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Rosenbrock23.C
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24 \*---------------------------------------------------------------------------*/
25 
26 #include "Rosenbrock23.H"
28 
29 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
30 
31 namespace Foam
32 {
33  defineTypeNameAndDebug(Rosenbrock23, 0);
34  addToRunTimeSelectionTable(ODESolver, Rosenbrock23, dictionary);
35 
36 const scalar
37  Rosenbrock23::a21 = 1,
38  Rosenbrock23::a31 = 1,
39  Rosenbrock23::a32 = 0,
40 
41  Rosenbrock23::c21 = -1.0156171083877702091975600115545,
42  Rosenbrock23::c31 = 4.0759956452537699824805835358067,
43  Rosenbrock23::c32 = 9.2076794298330791242156818474003,
44 
45  Rosenbrock23::b1 = 1,
46  Rosenbrock23::b2 = 6.1697947043828245592553615689730,
47  Rosenbrock23::b3 = -0.4277225654321857332623837380651,
48 
49  Rosenbrock23::e1 = 0.5,
50  Rosenbrock23::e2 = -2.9079558716805469821718236208017,
51  Rosenbrock23::e3 = 0.2235406989781156962736090927619,
52 
53  Rosenbrock23::gamma = 0.43586652150845899941601945119356,
54  Rosenbrock23::c2 = 0.43586652150845899941601945119356,
55 
56  Rosenbrock23::d1 = 0.43586652150845899941601945119356,
57  Rosenbrock23::d2 = 0.24291996454816804366592249683314,
58  Rosenbrock23::d3 = 2.1851380027664058511513169485832;
59 }
60 
61 
62 // * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
63 
65 :
66  ODESolver(ode, dict),
67  adaptiveSolver(ode, dict),
68  k1_(n_),
69  k2_(n_),
70  k3_(n_),
71  err_(n_),
72  dydx_(n_),
73  dfdx_(n_),
74  dfdy_(n_, n_),
75  a_(n_, n_),
76  pivotIndices_(n_)
77 {}
78 
79 
80 // * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
81 
83 {
84  if (ODESolver::resize())
85  {
87 
88  resizeField(k1_);
89  resizeField(k2_);
90  resizeField(k3_);
91  resizeField(err_);
92  resizeField(dydx_);
93  resizeField(dfdx_);
94  resizeMatrix(dfdy_);
95  resizeMatrix(a_);
96  resizeField(pivotIndices_);
97 
98  return true;
99  }
100  else
101  {
102  return false;
103  }
104 }
105 
106 
107 Foam::scalar Foam::Rosenbrock23::solve
108 (
109  const scalar x0,
110  const scalarField& y0,
111  const label li,
112  const scalarField& dydx0,
113  const scalar dx,
114  scalarField& y
115 ) const
116 {
117  odes_.jacobian(x0, y0, li, dfdx_, dfdy_);
118 
119  for (label i=0; i<n_; i++)
120  {
121  for (label j=0; j<n_; j++)
122  {
123  a_(i, j) = -dfdy_(i, j);
124  }
125 
126  a_(i, i) += 1.0/(gamma*dx);
127  }
128 
129  LUDecompose(a_, pivotIndices_);
130 
131  // Calculate k1:
132  forAll(k1_, i)
133  {
134  k1_[i] = dydx0[i] + dx*d1*dfdx_[i];
135  }
136 
137  LUBacksubstitute(a_, pivotIndices_, k1_);
138 
139  // Calculate k2:
140  forAll(y, i)
141  {
142  y[i] = y0[i] + a21*k1_[i];
143  }
144 
145  odes_.derivatives(x0 + c2*dx, y, li, dydx_);
146 
147  forAll(k2_, i)
148  {
149  k2_[i] = dydx_[i] + dx*d2*dfdx_[i] + c21*k1_[i]/dx;
150  }
151 
152  LUBacksubstitute(a_, pivotIndices_, k2_);
153 
154  // Calculate k3:
155  forAll(k3_, i)
156  {
157  k3_[i] = dydx_[i] + dx*d3*dfdx_[i]
158  + (c31*k1_[i] + c32*k2_[i])/dx;
159  }
160 
161  LUBacksubstitute(a_, pivotIndices_, k3_);
162 
163  // Calculate error and update state:
164  forAll(y, i)
165  {
166  y[i] = y0[i] + b1*k1_[i] + b2*k2_[i] + b3*k3_[i];
167  err_[i] = e1*k1_[i] + e2*k2_[i] + e3*k3_[i];
168  }
169 
170  return normaliseError(y0, y, err_);
171 }
172 
173 
175 (
176  scalar& x,
177  scalarField& y,
178  const label li,
179  scalar& dxTry
180 ) const
181 {
182  adaptiveSolver::solve(odes_, x, y, li, dxTry);
183 }
184 
185 
186 // ************************************************************************* //
dictionary dict
#define forAll(list, i)
Loop across all elements in list.
Definition: UList.H:434
Abstract base class for the systems of ordinary differential equations.
Definition: ODESystem.H:46
virtual bool resize()=0
Resize the ODE solver.
Definition: ODESolver.C:89
A list of keyword definitions, which are a keyword followed by any number of values (e...
Definition: dictionary.H:156
void LUDecompose(scalarSquareMatrix &matrix, labelList &pivotIndices)
LU decompose the matrix with pivoting.
virtual void derivatives(const scalar x, const scalarField &y, const label li, scalarField &dydx) const =0
Calculate the derivatives in dydx.
An ODE solver for chemistry.
Definition: ode.H:50
scalar normaliseError(const scalarField &y0, const scalarField &y, const scalarField &err) const
Return the normalised scalar error.
Definition: ODESolver.C:40
Macros for easy insertion into run-time selection tables.
bool resize(const label n)
Resize the ODE solver.
void resizeMatrix(scalarSquareMatrix &m) const
Definition: ODESolverI.H:61
const ODESystem & odes_
Reference to ODESystem.
Definition: ODESolver.H:58
Rosenbrock23(const ODESystem &ode, const dictionary &dict)
Construct from ODESystem.
Definition: Rosenbrock23.C:64
virtual scalar solve(const scalar x0, const scalarField &y0, const label li, const scalarField &dydx0, const scalar dx, scalarField &y) const
Solve a single step dx and return the error.
Definition: Rosenbrock23.C:108
virtual bool resize()
Resize the ODE solver.
Definition: Rosenbrock23.C:82
addToRunTimeSelectionTable(ensightPart, ensightPartCells, istream)
defineTypeNameAndDebug(combustionModel, 0)
Abstract base-class for ODE system solvers.
Definition: ODESolver.H:50
virtual void jacobian(const scalar x, const scalarField &y, const label li, scalarField &dfdx, scalarSquareMatrix &dfdy) const =0
Calculate the Jacobian of the system.
static void resizeField(UList< Type > &f, const label n)
Definition: ODESolverI.H:48
virtual scalar solve(const scalar x0, const scalarField &y0, const label li, const scalarField &dydx0, const scalar dx, scalarField &y) const =0
Solve a single step dx and return the error.
label n_
Size of the ODESystem (adjustable)
Definition: ODESolver.H:64
Namespace for OpenFOAM.
void LUBacksubstitute(const scalarSquareMatrix &luMmatrix, const labelList &pivotIndices, List< Type > &source)
LU back-substitution with given source, returning the solution.