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 
95 Foam::scalar Foam::RKDP45::solve
96 (
97  const scalar x0,
98  const scalarField& y0,
99  const scalarField& dydx0,
100  const scalar dx,
101  scalarField& y
102 ) const
103 {
104  forAll(yTemp_, i)
105  {
106  yTemp_[i] = y0[i] + a21*dx*dydx0[i];
107  }
108 
109  odes_.derivatives(x0 + c2*dx, yTemp_, k2_);
110 
111  forAll(yTemp_, i)
112  {
113  yTemp_[i] = y0[i] + dx*(a31*dydx0[i] + a32*k2_[i]);
114  }
115 
116  odes_.derivatives(x0 + c3*dx, yTemp_, k3_);
117 
118  forAll(yTemp_, i)
119  {
120  yTemp_[i] = y0[i] + dx*(a41*dydx0[i] + a42*k2_[i] + a43*k3_[i]);
121  }
122 
123  odes_.derivatives(x0 + c4*dx, yTemp_, k4_);
124 
125  forAll(yTemp_, i)
126  {
127  yTemp_[i] = y0[i]
128  + dx*(a51*dydx0[i] + a52*k2_[i] + a53*k3_[i] + a54*k4_[i]);
129  }
130 
131  odes_.derivatives(x0 + c5*dx, yTemp_, k5_);
132 
133  forAll(yTemp_, i)
134  {
135  yTemp_[i] = y0[i]
136  + dx
137  *(a61*dydx0[i] + a62*k2_[i] + a63*k3_[i] + a64*k4_[i] + a65*k5_[i]);
138  }
139 
140  odes_.derivatives(x0 + dx, yTemp_, k6_);
141 
142  forAll(y, i)
143  {
144  y[i] = y0[i]
145  + dx*(b1*dydx0[i] + b3*k3_[i] + b4*k4_[i] + b5*k5_[i] + b6*k6_[i]);
146  }
147 
148  // Reuse k2_ for the derivative of the new state
149  odes_.derivatives(x0 + dx, y, k2_);
150 
151  forAll(err_, i)
152  {
153  err_[i] =
154  dx
155  *(e1*dydx0[i] + e3*k3_[i] + e4*k4_[i] + e5*k5_[i] + e6*k6_[i]
156  + e7*k2_[i]);
157  }
158 
159  return normalizeError(y0, y, err_);
160 }
161 
162 
164 (
165  scalar& x,
166  scalarField& y,
167  scalar& dxTry
168 ) const
169 {
170  adaptiveSolver::solve(odes_, x, y, dxTry);
171 }
172 
173 
174 // ************************************************************************* //
RKDP45(const ODESystem &ode, const dictionary &dict)
Construct from ODE.
Definition: RKDP45.C:79
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:96
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.
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)