Rosenbrock23.C
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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 
82 Foam::scalar Foam::Rosenbrock23::solve
83 (
84  const scalar x0,
85  const scalarField& y0,
86  const scalarField& dydx0,
87  const scalar dx,
88  scalarField& y
89 ) const
90 {
91  odes_.jacobian(x0, y0, dfdx_, dfdy_);
92 
93  for (label i=0; i<n_; i++)
94  {
95  for (label j=0; j<n_; j++)
96  {
97  a_[i][j] = -dfdy_[i][j];
98  }
99 
100  a_[i][i] += 1.0/(gamma*dx);
101  }
102 
103  LUDecompose(a_, pivotIndices_);
104 
105  // Calculate k1:
106  forAll(k1_, i)
107  {
108  k1_[i] = dydx0[i] + dx*d1*dfdx_[i];
109  }
110 
111  LUBacksubstitute(a_, pivotIndices_, k1_);
112 
113  // Calculate k2:
114  forAll(y, i)
115  {
116  y[i] = y0[i] + a21*k1_[i];
117  }
118 
119  odes_.derivatives(x0 + c2*dx, y, dydx_);
120 
121  forAll(k2_, i)
122  {
123  k2_[i] = dydx_[i] + dx*d2*dfdx_[i] + c21*k1_[i]/dx;
124  }
125 
126  LUBacksubstitute(a_, pivotIndices_, k2_);
127 
128  // Calculate k3:
129  forAll(k3_, i)
130  {
131  k3_[i] = dydx_[i] + dx*d3*dfdx_[i]
132  + (c31*k1_[i] + c32*k2_[i])/dx;
133  }
134 
135  LUBacksubstitute(a_, pivotIndices_, k3_);
136 
137  // Calculate error and update state:
138  forAll(y, i)
139  {
140  y[i] = y0[i] + b1*k1_[i] + b2*k2_[i] + b3*k3_[i];
141  err_[i] = e1*k1_[i] + e2*k2_[i] + e3*k3_[i];
142  }
143 
144  return normalizeError(y0, y, err_);
145 }
146 
147 
149 (
150  scalar& x,
151  scalarField& y,
152  scalar& dxTry
153 ) const
154 {
155  adaptiveSolver::solve(odes_, x, y, dxTry);
156 }
157 
158 
159 // ************************************************************************* //
void LUBacksubstitute(const scalarSquareMatrix &luMmatrix, const labelList &pivotIndices, List< Type > &source)
LU back-substitution with given source, returning the solution.
label n_
Size of the ODESystem.
Definition: ODESolver.H:61
virtual scalar solve(const scalar x0, const scalarField &y0, const scalarField &dydx0, const scalar dx, scalarField &y) const =0
Solve a single step dx and return the error.
intWM_LABEL_SIZE_t label
A label is an int32_t or int64_t as specified by the pre-processor macro WM_LABEL_SIZE.
Definition: label.H:59
A list of keyword definitions, which are a keyword followed by any number of values (e...
Definition: dictionary.H:137
virtual void derivatives(const scalar x, const scalarField &y, scalarField &dydx) const =0
Calculate the derivatives in dydx.
Namespace for OpenFOAM.
Abstract base class for the systems of ordinary differential equations.
Definition: ODESystem.H:46
dictionary dict
An ODE solver for chemistry.
Definition: ode.H:50
#define forAll(list, i)
Definition: UList.H:421
const ODESystem & odes_
Reference to ODESystem.
Definition: ODESolver.H:58
Macros for easy insertion into run-time selection tables.
Abstract base-class for ODE system solvers.
Definition: ODESolver.H:50
Rosenbrock23(const ODESystem &ode, const dictionary &dict)
Construct from ODE.
Definition: Rosenbrock23.C:64
virtual void jacobian(const scalar x, const scalarField &y, scalarField &dfdx, scalarSquareMatrix &dfdy) const =0
Calculate the Jacobian of the system.
scalar solve(const scalar x0, const scalarField &y0, const scalarField &dydx0, const scalar dx, scalarField &y) const
Solve a single step dx and return the error.
Definition: Rosenbrock23.C:83
scalar normalizeError(const scalarField &y0, const scalarField &y, const scalarField &err) const
Return the nomalized scalar error.
Definition: ODESolver.C:67
void LUDecompose(scalarSquareMatrix &matrix, labelList &pivotIndices)
LU decompose the matrix with pivoting.
addToRunTimeSelectionTable(ensightPart, ensightPartCells, istream)
defineTypeNameAndDebug(combustionModel, 0)