rodas23.C
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25 
26 #include "rodas23.H"
28 
29 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
30 
31 namespace Foam
32 {
33  defineTypeNameAndDebug(rodas23, 0);
34  addToRunTimeSelectionTable(ODESolver, rodas23, dictionary);
35 
36 const scalar
37  rodas23::c3 = 1,
38  rodas23::d1 = 1.0/2.0,
39  rodas23::d2 = 3.0/2.0,
40  rodas23::a31 = 2,
41  rodas23::a41 = 2,
42  rodas23::c21 = 4,
43  rodas23::c31 = 1,
44  rodas23::c32 = -1,
45  rodas23::c41 = 1,
46  rodas23::c42 = -1,
47  rodas23::c43 = -8.0/3.0,
48  rodas23::gamma = 1.0/2.0;
49 }
50 
51 
52 // * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
53 
55 :
56  ODESolver(ode, dict),
57  adaptiveSolver(ode, dict),
58  k1_(n_),
59  k2_(n_),
60  k3_(n_),
61  dy_(n_),
62  err_(n_),
63  dydx_(n_),
64  dfdx_(n_),
65  dfdy_(n_, n_),
66  a_(n_, n_),
67  pivotIndices_(n_)
68 {}
69 
70 
71 // * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
72 
73 Foam::scalar Foam::rodas23::solve
74 (
75  const scalar x0,
76  const scalarField& y0,
77  const scalarField& dydx0,
78  const scalar dx,
79  scalarField& y
80 ) const
81 {
82  odes_.jacobian(x0, y0, dfdx_, dfdy_);
83 
84  for (label i=0; i<n_; i++)
85  {
86  for (label j=0; j<n_; j++)
87  {
88  a_[i][j] = -dfdy_[i][j];
89  }
90 
91  a_[i][i] += 1.0/(gamma*dx);
92  }
93 
94  LUDecompose(a_, pivotIndices_);
95 
96  // Calculate k1:
97  forAll(k1_, i)
98  {
99  k1_[i] = dydx0[i] + dx*d1*dfdx_[i];
100  }
101 
102  LUBacksubstitute(a_, pivotIndices_, k1_);
103 
104  // Calculate k2:
105  forAll(k2_, i)
106  {
107  k2_[i] = dydx0[i] + dx*d2*dfdx_[i] + c21*k1_[i]/dx;
108  }
109 
110  LUBacksubstitute(a_, pivotIndices_, k2_);
111 
112  // Calculate k3:
113  forAll(y, i)
114  {
115  dy_[i] = a31*k1_[i];
116  y[i] = y0[i] + dy_[i];
117  }
118 
119  odes_.derivatives(x0 + dx, y, dydx_);
120 
121  forAll(k3_, i)
122  {
123  k3_[i] = dydx_[i] + (c31*k1_[i] + c32*k2_[i])/dx;
124  }
125 
126  LUBacksubstitute(a_, pivotIndices_, k3_);
127 
128  // Calculate new state and error
129  forAll(y, i)
130  {
131  dy_[i] += k3_[i];
132  y[i] = y0[i] + dy_[i];
133  }
134 
135  odes_.derivatives(x0 + dx, y, dydx_);
136 
137  forAll(err_, i)
138  {
139  err_[i] = dydx_[i] + (c41*k1_[i] + c42*k2_[i] + c43*k3_[i])/dx;
140  }
141 
142  LUBacksubstitute(a_, pivotIndices_, err_);
143 
144  forAll(y, i)
145  {
146  y[i] = y0[i] + dy_[i] + err_[i];
147  }
148 
149  return normalizeError(y0, y, err_);
150 }
151 
152 
154 (
155  scalar& x,
156  scalarField& y,
157  scalar& dxTry
158 ) const
159 {
160  adaptiveSolver::solve(odes_, x, y, dxTry);
161 }
162 
163 
164 // ************************************************************************* //
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.
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: rodas23.C:74
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
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)
rodas23(const ODESystem &ode, const dictionary &dict)
Construct from ODE.
Definition: rodas23.C:54