RKDP45.C
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25 
26 #include "RKDP45.H"
28 
29 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
30 
31 namespace Foam
32 {
33  defineTypeNameAndDebug(RKDP45, 0);
34  addToRunTimeSelectionTable(ODESolver, RKDP45, dictionary);
35 
36 const scalar
37  RKDP45::c2 = 1.0/5.0,
38  RKDP45::c3 = 3.0/10.0,
39  RKDP45::c4 = 4.0/5.0,
40  RKDP45::c5 = 8.0/9.0,
41 
42  RKDP45::a21 = 1.0/5.0,
43 
44  RKDP45::a31 = 3.0/40.0,
45  RKDP45::a32 = 9.0/40.0,
46 
47  RKDP45::a41 = 44.0/45.0,
48  RKDP45::a42 = -56.0/15.0,
49  RKDP45::a43 = 32.0/9.0,
50 
51  RKDP45::a51 = 19372.0/6561.0,
52  RKDP45::a52 = -25360.0/2187.0,
53  RKDP45::a53 = 64448.0/6561.0,
54  RKDP45::a54 = -212.0/729.0,
55 
56  RKDP45::a61 = 9017.0/3168.0,
57  RKDP45::a62 = -355.0/33.0,
58  RKDP45::a63 = 46732.0/5247.0,
59  RKDP45::a64 = 49.0/176.0,
60  RKDP45::a65 = -5103.0/18656.0,
61 
62  RKDP45::b1 = 35.0/384.0,
63  RKDP45::b3 = 500.0/1113.0,
64  RKDP45::b4 = 125.0/192.0,
65  RKDP45::b5 = -2187.0/6784.0,
66  RKDP45::b6 = 11.0/84.0,
67 
68  RKDP45::e1 = 5179.0/57600.0 - RKDP45::b1,
69  RKDP45::e3 = 7571.0/16695.0 - RKDP45::b3,
70  RKDP45::e4 = 393.0/640.0 - RKDP45::b4,
71  RKDP45::e5 = -92097.0/339200.0 - RKDP45::b5,
72  RKDP45::e6 = 187.0/2100.0 - RKDP45::b6,
73  RKDP45::e7 = 1.0/40.0;
74 }
75 
76 
77 // * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
78 
80 :
81  ODESolver(ode, dict),
82  adaptiveSolver(ode, dict),
83  yTemp_(n_),
84  k2_(n_),
85  k3_(n_),
86  k4_(n_),
87  k5_(n_),
88  k6_(n_),
89  err_(n_)
90 {}
91 
92 
93 // * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
94 
96 {
97  if (ODESolver::resize())
98  {
100 
101  resizeField(yTemp_);
102  resizeField(k2_);
103  resizeField(k3_);
104  resizeField(k4_);
105  resizeField(k5_);
106  resizeField(k6_);
107  resizeField(err_);
108 
109  return true;
110  }
111  else
112  {
113  return false;
114  }
115 }
116 
117 
118 Foam::scalar Foam::RKDP45::solve
119 (
120  const scalar x0,
121  const scalarField& y0,
122  const scalarField& dydx0,
123  const scalar dx,
124  scalarField& y
125 ) const
126 {
127  forAll(yTemp_, i)
128  {
129  yTemp_[i] = y0[i] + a21*dx*dydx0[i];
130  }
131 
132  odes_.derivatives(x0 + c2*dx, yTemp_, k2_);
133 
134  forAll(yTemp_, i)
135  {
136  yTemp_[i] = y0[i] + dx*(a31*dydx0[i] + a32*k2_[i]);
137  }
138 
139  odes_.derivatives(x0 + c3*dx, yTemp_, k3_);
140 
141  forAll(yTemp_, i)
142  {
143  yTemp_[i] = y0[i] + dx*(a41*dydx0[i] + a42*k2_[i] + a43*k3_[i]);
144  }
145 
146  odes_.derivatives(x0 + c4*dx, yTemp_, k4_);
147 
148  forAll(yTemp_, i)
149  {
150  yTemp_[i] = y0[i]
151  + dx*(a51*dydx0[i] + a52*k2_[i] + a53*k3_[i] + a54*k4_[i]);
152  }
153 
154  odes_.derivatives(x0 + c5*dx, yTemp_, k5_);
155 
156  forAll(yTemp_, i)
157  {
158  yTemp_[i] = y0[i]
159  + dx
160  *(a61*dydx0[i] + a62*k2_[i] + a63*k3_[i] + a64*k4_[i] + a65*k5_[i]);
161  }
162 
163  odes_.derivatives(x0 + dx, yTemp_, k6_);
164 
165  forAll(y, i)
166  {
167  y[i] = y0[i]
168  + dx*(b1*dydx0[i] + b3*k3_[i] + b4*k4_[i] + b5*k5_[i] + b6*k6_[i]);
169  }
170 
171  // Reuse k2_ for the derivative of the new state
172  odes_.derivatives(x0 + dx, y, k2_);
173 
174  forAll(err_, i)
175  {
176  err_[i] =
177  dx
178  *(e1*dydx0[i] + e3*k3_[i] + e4*k4_[i] + e5*k5_[i] + e6*k6_[i]
179  + e7*k2_[i]);
180  }
181 
182  return normalizeError(y0, y, err_);
183 }
184 
185 
187 (
188  scalar& x,
189  scalarField& y,
190  scalar& dxTry
191 ) const
192 {
193  adaptiveSolver::solve(odes_, x, y, dxTry);
194 }
195 
196 
197 // ************************************************************************* //
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.
dictionary dict
#define forAll(list, i)
Loop across all elements in list.
Definition: UList.H:428
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:137
An ODE solver for chemistry.
Definition: ode.H:50
Macros for easy insertion into run-time selection tables.
virtual bool resize()
Resize the ODE solver.
Definition: RKDP45.C:95
bool resize(const label n)
Resize the ODE solver.
const ODESystem & odes_
Reference to ODESystem.
Definition: ODESolver.H:58
addToRunTimeSelectionTable(ensightPart, ensightPartCells, istream)
RKDP45(const ODESystem &ode, const dictionary &dict)
Construct from ODESystem.
Definition: RKDP45.C:79
defineTypeNameAndDebug(combustionModel, 0)
virtual 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: RKDP45.C:119
scalar normalizeError(const scalarField &y0, const scalarField &y, const scalarField &err) const
Return the nomalized scalar error.
Definition: ODESolver.C:40
Abstract base-class for ODE system solvers.
Definition: ODESolver.H:50
static void resizeField(UList< Type > &f, const label n)
Definition: ODESolverI.H:48
label n_
Size of the ODESystem (adjustable)
Definition: ODESolver.H:64
virtual void derivatives(const scalar x, const scalarField &y, scalarField &dydx) const =0
Calculate the derivatives in dydx.
Namespace for OpenFOAM.