Rosenbrock12.C
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25 
26 #include "Rosenbrock12.H"
28 
29 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
30 
31 namespace Foam
32 {
33  defineTypeNameAndDebug(Rosenbrock12, 0);
34  addToRunTimeSelectionTable(ODESolver, Rosenbrock12, dictionary);
35 
36 const scalar
37  Rosenbrock12::gamma = 1 + 1.0/std::sqrt(2.0),
38  Rosenbrock12::a21 = 1.0/gamma,
39  Rosenbrock12::c2 = 1.0,
40  Rosenbrock12::c21 = -2.0/gamma,
41  Rosenbrock12::b1 = (3.0/2.0)/gamma,
42  Rosenbrock12::b2 = (1.0/2.0)/gamma,
43  Rosenbrock12::e1 = b1 - 1.0/gamma,
44  Rosenbrock12::e2 = b2,
45  Rosenbrock12::d1 = gamma,
46  Rosenbrock12::d2 = -gamma;
47 }
48 
49 
50 // * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
51 
53 :
54  ODESolver(ode, dict),
55  adaptiveSolver(ode, dict),
56  k1_(n_),
57  k2_(n_),
58  err_(n_),
59  dydx_(n_),
60  dfdx_(n_),
61  dfdy_(n_, n_),
62  a_(n_, n_),
63  pivotIndices_(n_)
64 {}
65 
66 
67 // * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
68 
69 Foam::scalar Foam::Rosenbrock12::solve
70 (
71  const scalar x0,
72  const scalarField& y0,
73  const scalarField& dydx0,
74  const scalar dx,
75  scalarField& y
76 ) const
77 {
78  odes_.jacobian(x0, y0, dfdx_, dfdy_);
79 
80  for (label i=0; i<n_; i++)
81  {
82  for (label j=0; j<n_; j++)
83  {
84  a_[i][j] = -dfdy_[i][j];
85  }
86 
87  a_[i][i] += 1.0/(gamma*dx);
88  }
89 
90  LUDecompose(a_, pivotIndices_);
91 
92  // Calculate k1:
93  forAll(k1_, i)
94  {
95  k1_[i] = dydx0[i] + dx*d1*dfdx_[i];
96  }
97 
98  LUBacksubstitute(a_, pivotIndices_, k1_);
99 
100  // Calculate k2:
101  forAll(y, i)
102  {
103  y[i] = y0[i] + a21*k1_[i];
104  }
105 
106  odes_.derivatives(x0 + c2*dx, y, dydx_);
107 
108  forAll(k2_, i)
109  {
110  k2_[i] = dydx_[i] + dx*d2*dfdx_[i] + c21*k1_[i]/dx;
111  }
112 
113  LUBacksubstitute(a_, pivotIndices_, k2_);
114 
115  // Calculate error and update state:
116  forAll(y, i)
117  {
118  y[i] = y0[i] + b1*k1_[i] + b2*k2_[i];
119  err_[i] = e1*k1_[i] + e2*k2_[i];
120  }
121 
122  return normalizeError(y0, y, err_);
123 }
124 
125 
127 (
128  scalar& x,
129  scalarField& y,
130  scalar& dxTry
131 ) const
132 {
133  adaptiveSolver::solve(odes_, x, y, dxTry);
134 }
135 
136 
137 // ************************************************************************* //
dimensionedScalar sqrt(const dimensionedScalar &ds)
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
Rosenbrock12(const ODESystem &ode, const dictionary &dict)
Construct from ODE.
Definition: Rosenbrock12.C:52
#define forAll(list, i)
Definition: UList.H:421
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: Rosenbrock12.C:70
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
virtual void jacobian(const scalar x, const scalarField &y, scalarField &dfdx, scalarSquareMatrix &dfdy) const =0
Calculate the Jacobian of the system.
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)