RKCK45.C
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25 
26 #include "RKCK45.H"
28 
29 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
30 
31 namespace Foam
32 {
33  defineTypeNameAndDebug(RKCK45, 0);
34  addToRunTimeSelectionTable(ODESolver, RKCK45, dictionary);
35 
36 const scalar
37  RKCK45::c2 = 1.0/5.0,
38  RKCK45::c3 = 3.0/10.0,
39  RKCK45::c4 = 3.0/5.0,
40  RKCK45::c5 = 1.0,
41  RKCK45::c6 = 7.0/8.0,
42 
43  RKCK45::a21 = 1.0/5.0,
44  RKCK45::a31 = 3.0/40.0,
45  RKCK45::a32 = 9.0/40.0,
46  RKCK45::a41 = 3.0/10.0,
47  RKCK45::a42 = -9.0/10.0,
48  RKCK45::a43 = 6.0/5.0,
49  RKCK45::a51 = -11.0/54.0,
50  RKCK45::a52 = 5.0/2.0,
51  RKCK45::a53 = -70.0/27.0,
52  RKCK45::a54 = 35.0/27.0,
53  RKCK45::a61 = 1631.0/55296.0,
54  RKCK45::a62 = 175.0/512.0,
55  RKCK45::a63 = 575.0/13824.0,
56  RKCK45::a64 = 44275.0/110592.0,
57  RKCK45::a65 = 253.0/4096.0,
58 
59  RKCK45::b1 = 37.0/378.0,
60  RKCK45::b3 = 250.0/621.0,
61  RKCK45::b4 = 125.0/594.0,
62  RKCK45::b6 = 512.0/1771.0,
63 
64  RKCK45::e1 = RKCK45::b1 - 2825.0/27648.0,
65  RKCK45::e3 = RKCK45::b3 - 18575.0/48384.0,
66  RKCK45::e4 = RKCK45::b4 - 13525.0/55296.0,
67  RKCK45::e5 = -277.00/14336.0,
68  RKCK45::e6 = RKCK45::b6 - 0.25;
69 }
70 
71 
72 // * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
73 
75 :
76  ODESolver(ode, dict),
77  adaptiveSolver(ode, dict),
78  yTemp_(n_),
79  k2_(n_),
80  k3_(n_),
81  k4_(n_),
82  k5_(n_),
83  k6_(n_),
84  err_(n_)
85 {}
86 
87 
88 // * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
89 
90 Foam::scalar Foam::RKCK45::solve
91 (
92  const scalar x0,
93  const scalarField& y0,
94  const scalarField& dydx0,
95  const scalar dx,
96  scalarField& y
97 ) const
98 {
99  forAll(yTemp_, i)
100  {
101  yTemp_[i] = y0[i] + a21*dx*dydx0[i];
102  }
103 
104  odes_.derivatives(x0 + c2*dx, yTemp_, k2_);
105 
106  forAll(yTemp_, i)
107  {
108  yTemp_[i] = y0[i] + dx*(a31*dydx0[i] + a32*k2_[i]);
109  }
110 
111  odes_.derivatives(x0 + c3*dx, yTemp_, k3_);
112 
113  forAll(yTemp_, i)
114  {
115  yTemp_[i] = y0[i] + dx*(a41*dydx0[i] + a42*k2_[i] + a43*k3_[i]);
116  }
117 
118  odes_.derivatives(x0 + c4*dx, yTemp_, k4_);
119 
120  forAll(yTemp_, i)
121  {
122  yTemp_[i] = y0[i]
123  + dx*(a51*dydx0[i] + a52*k2_[i] + a53*k3_[i] + a54*k4_[i]);
124  }
125 
126  odes_.derivatives(x0 + c5*dx, yTemp_, k5_);
127 
128  forAll(yTemp_, i)
129  {
130  yTemp_[i] = y0[i]
131  + dx
132  *(a61*dydx0[i] + a62*k2_[i] + a63*k3_[i] + a64*k4_[i] + a65*k5_[i]);
133  }
134 
135  odes_.derivatives(x0 + c6*dx, yTemp_, k6_);
136 
137  forAll(y, i)
138  {
139  y[i] = y0[i]
140  + dx*(b1*dydx0[i] + b3*k3_[i] + b4*k4_[i] + b6*k6_[i]);
141  }
142 
143  forAll(err_, i)
144  {
145  err_[i] =
146  dx
147  *(e1*dydx0[i] + e3*k3_[i] + e4*k4_[i] + e5*k5_[i] + e6*k6_[i]);
148  }
149 
150  return normalizeError(y0, y, err_);
151 }
152 
153 
155 (
156  scalar& x,
157  scalarField& y,
158  scalar& dxTry
159 ) const
160 {
161  adaptiveSolver::solve(odes_, x, y, dxTry);
162 }
163 
164 
165 // ************************************************************************* //
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: RKCK45.C:91
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.
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.
RKCK45(const ODESystem &ode, const dictionary &dict)
Construct from ODE.
Definition: RKCK45.C:74
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
scalar normalizeError(const scalarField &y0, const scalarField &y, const scalarField &err) const
Return the nomalized scalar error.
Definition: ODESolver.C:67
addToRunTimeSelectionTable(ensightPart, ensightPartCells, istream)
defineTypeNameAndDebug(combustionModel, 0)