RKF45.C
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25 
26 #include "RKF45.H"
28 
29 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
30 
31 namespace Foam
32 {
35 
36 const scalar
37  RKF45::c2 = 1.0/4.0,
38  RKF45::c3 = 3.0/8.0,
39  RKF45::c4 = 12.0/13.0,
40  RKF45::c5 = 1.0,
41  RKF45::c6 = 1.0/2.0,
42 
43  RKF45::a21 = 1.0/4.0,
44  RKF45::a31 = 3.0/32.0,
45  RKF45::a32 = 9.0/32.0,
46  RKF45::a41 = 1932.0/2197.0,
47  RKF45::a42 = -7200.0/2197.0,
48  RKF45::a43 = 7296.0/2197.0,
49  RKF45::a51 = 439.0/216.0,
50  RKF45::a52 = -8.0,
51  RKF45::a53 = 3680.0/513.0,
52  RKF45::a54 = -845.0/4104.0,
53  RKF45::a61 = -8.0/27.0,
54  RKF45::a62 = 2.0,
55  RKF45::a63 = -3544.0/2565.0,
56  RKF45::a64 = 1859.0/4104.0,
57  RKF45::a65 = -11.0/40.0,
58 
59  RKF45::b1 = 16.0/135.0,
60  RKF45::b3 = 6656.0/12825.0,
61  RKF45::b4 = 28561.0/56430.0,
62  RKF45::b5 = -9.0/50.0,
63  RKF45::b6 = 2.0/55.0,
64 
65  RKF45::e1 = 25.0/216.0 - RKF45::b1,
66  RKF45::e3 = 1408.0/2565.0 - RKF45::b3,
67  RKF45::e4 = 2197.0/4104.0 - RKF45::b4,
68  RKF45::e5 = -1.0/5.0 - RKF45::b5,
69  RKF45::e6 = -RKF45::b6;
70 }
71 
72 
73 // * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
74 
76 :
77  ODESolver(ode, dict),
79  yTemp_(n_),
80  k2_(n_),
81  k3_(n_),
82  k4_(n_),
83  k5_(n_),
84  k6_(n_),
85  err_(n_)
86 {}
87 
88 
89 // * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
90 
92 {
93  if (ODESolver::resize())
94  {
96 
97  resizeField(yTemp_);
98  resizeField(k2_);
99  resizeField(k3_);
100  resizeField(k4_);
101  resizeField(k5_);
102  resizeField(k6_);
103  resizeField(err_);
104 
105  return true;
106  }
107  else
108  {
109  return false;
110  }
111 }
112 
113 
114 Foam::scalar Foam::RKF45::solve
115 (
116  const scalar x0,
117  const scalarField& y0,
118  const label li,
119  const scalarField& dydx0,
120  const scalar dx,
121  scalarField& y
122 ) const
123 {
124  forAll(yTemp_, i)
125  {
126  yTemp_[i] = y0[i] + a21*dx*dydx0[i];
127  }
128 
129  odes_.derivatives(x0 + c2*dx, yTemp_, li, k2_);
130 
131  forAll(yTemp_, i)
132  {
133  yTemp_[i] = y0[i] + dx*(a31*dydx0[i] + a32*k2_[i]);
134  }
135 
136  odes_.derivatives(x0 + c3*dx, yTemp_, li, k3_);
137 
138  forAll(yTemp_, i)
139  {
140  yTemp_[i] = y0[i] + dx*(a41*dydx0[i] + a42*k2_[i] + a43*k3_[i]);
141  }
142 
143  odes_.derivatives(x0 + c4*dx, yTemp_, li, k4_);
144 
145  forAll(yTemp_, i)
146  {
147  yTemp_[i] = y0[i]
148  + dx*(a51*dydx0[i] + a52*k2_[i] + a53*k3_[i] + a54*k4_[i]);
149  }
150 
151  odes_.derivatives(x0 + c5*dx, yTemp_, li, k5_);
152 
153  forAll(yTemp_, i)
154  {
155  yTemp_[i] = y0[i]
156  + dx
157  *(a61*dydx0[i] + a62*k2_[i] + a63*k3_[i] + a64*k4_[i] + a65*k5_[i]);
158  }
159 
160  odes_.derivatives(x0 + c6*dx, yTemp_, li, k6_);
161 
162  // Calculate the 5th-order solution
163  forAll(y, i)
164  {
165  y[i] = y0[i]
166  + dx
167  *(b1*dydx0[i] + b3*k3_[i] + b4*k4_[i] + b5*k5_[i] + b6*k6_[i]);
168  }
169 
170  // Calculate the error estimate from the difference between the
171  // 4th-order and 5th-order solutions
172  forAll(err_, i)
173  {
174  err_[i] =
175  dx
176  *(e1*dydx0[i] + e3*k3_[i] + e4*k4_[i] + e5*k5_[i] + e6*k6_[i]);
177  }
178 
179  return normaliseError(y0, y, err_);
180 }
181 
182 
184 (
185  scalar& x,
186  scalarField& y,
187  const label li,
188  scalar& dxTry
189 ) const
190 {
191  adaptiveSolver::solve(odes_, x, y, li, dxTry);
192 }
193 
194 
195 // ************************************************************************* //
scalar y
#define forAll(list, i)
Loop across all elements in list.
Definition: UList.H:434
Macros for easy insertion into run-time selection tables.
Abstract base-class for ODE system solvers.
Definition: ODESolver.H:51
virtual bool resize()=0
Resize the ODE solver.
Definition: ODESolver.C:89
Abstract base class for the systems of ordinary differential equations.
Definition: ODESystem.H:47
4/5th Order Runge-Kutta-Fehlberg ODE solver
Definition: RKF45.H:70
virtual bool resize()
Resize the ODE solver.
Definition: RKF45.C:91
virtual void solve(scalar &x, scalarField &y, const label li, scalar &dxTry) const
Inherit solve from ODESolver.
Definition: ODESolver.C:116
RKF45(const ODESystem &ode, const dictionary &dict)
Construct from ODESystem.
Definition: RKF45.C:75
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.
bool resize(const label n)
Resize the ODE solver.
A list of keyword definitions, which are a keyword followed by any number of values (e....
Definition: dictionary.H:162
An ODE solver for chemistry.
Definition: ode.H:53
const dimensionedScalar c2
Second radiation constant: default SI units: [m K].
Namespace for OpenFOAM.
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
addToRunTimeSelectionTable(polyPatch, mergedCyclicPolyPatch, word)
dimensionedScalar y0(const dimensionedScalar &ds)
defineTypeNameAndDebug(combustionModel, 0)
dictionary dict