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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 
74 {
75  if (ODESolver::resize())
76  {
78 
79  resizeField(k1_);
80  resizeField(k2_);
81  resizeField(k3_);
82  resizeField(dy_);
83  resizeField(err_);
84  resizeField(dydx_);
85  resizeField(dfdx_);
86  resizeMatrix(dfdy_);
87  resizeMatrix(a_);
88  resizeField(pivotIndices_);
89 
90  return true;
91  }
92  else
93  {
94  return false;
95  }
96 }
97 
98 
99 Foam::scalar Foam::rodas23::solve
100 (
101  const scalar x0,
102  const scalarField& y0,
103  const label li,
104  const scalarField& dydx0,
105  const scalar dx,
106  scalarField& y
107 ) const
108 {
109  odes_.jacobian(x0, y0, li, dfdx_, dfdy_);
110 
111  for (label i=0; i<n_; i++)
112  {
113  for (label j=0; j<n_; j++)
114  {
115  a_(i, j) = -dfdy_(i, j);
116  }
117 
118  a_(i, i) += 1.0/(gamma*dx);
119  }
120 
121  LUDecompose(a_, pivotIndices_);
122 
123  // Calculate k1:
124  forAll(k1_, i)
125  {
126  k1_[i] = dydx0[i] + dx*d1*dfdx_[i];
127  }
128 
129  LUBacksubstitute(a_, pivotIndices_, k1_);
130 
131  // Calculate k2:
132  forAll(k2_, i)
133  {
134  k2_[i] = dydx0[i] + dx*d2*dfdx_[i] + c21*k1_[i]/dx;
135  }
136 
137  LUBacksubstitute(a_, pivotIndices_, k2_);
138 
139  // Calculate k3:
140  forAll(y, i)
141  {
142  dy_[i] = a31*k1_[i];
143  y[i] = y0[i] + dy_[i];
144  }
145 
146  odes_.derivatives(x0 + dx, y, li, dydx_);
147 
148  forAll(k3_, i)
149  {
150  k3_[i] = dydx_[i] + (c31*k1_[i] + c32*k2_[i])/dx;
151  }
152 
153  LUBacksubstitute(a_, pivotIndices_, k3_);
154 
155  // Calculate new state and error
156  forAll(y, i)
157  {
158  dy_[i] += k3_[i];
159  y[i] = y0[i] + dy_[i];
160  }
161 
162  odes_.derivatives(x0 + dx, y, li, dydx_);
163 
164  forAll(err_, i)
165  {
166  err_[i] = dydx_[i] + (c41*k1_[i] + c42*k2_[i] + c43*k3_[i])/dx;
167  }
168 
169  LUBacksubstitute(a_, pivotIndices_, err_);
170 
171  forAll(y, i)
172  {
173  y[i] = y0[i] + dy_[i] + err_[i];
174  }
175 
176  return normaliseError(y0, y, err_);
177 }
178 
179 
181 (
182  scalar& x,
183  scalarField& y,
184  const label li,
185  scalar& dxTry
186 ) const
187 {
188  adaptiveSolver::solve(odes_, x, y, li, dxTry);
189 }
190 
191 
192 // ************************************************************************* //
dictionary dict
#define forAll(list, i)
Loop across all elements in list.
Definition: UList.H:434
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
rodas23(const ODESystem &ode, const dictionary &dict)
Construct from ODESystem.
Definition: rodas23.C:54
virtual scalar solve(const scalar x0, const scalarField &y0, const label li, const scalarField &dydx0, const scalar dx, scalarField &y) const
Solve a single step dx and return the error.
Definition: rodas23.C:100
A list of keyword definitions, which are a keyword followed by any number of values (e...
Definition: dictionary.H:156
void LUDecompose(scalarSquareMatrix &matrix, labelList &pivotIndices)
LU decompose the matrix with pivoting.
virtual void derivatives(const scalar x, const scalarField &y, const label li, scalarField &dydx) const =0
Calculate the derivatives in dydx.
An ODE solver for chemistry.
Definition: ode.H:50
scalar normaliseError(const scalarField &y0, const scalarField &y, const scalarField &err) const
Return the normalised scalar error.
Definition: ODESolver.C:40
Macros for easy insertion into run-time selection tables.
bool resize(const label n)
Resize the ODE solver.
void resizeMatrix(scalarSquareMatrix &m) const
Definition: ODESolverI.H:61
const ODESystem & odes_
Reference to ODESystem.
Definition: ODESolver.H:58
addToRunTimeSelectionTable(ensightPart, ensightPartCells, istream)
virtual bool resize()
Resize the ODE solver.
Definition: rodas23.C:73
defineTypeNameAndDebug(combustionModel, 0)
Abstract base-class for ODE system solvers.
Definition: ODESolver.H:50
virtual void jacobian(const scalar x, const scalarField &y, const label li, scalarField &dfdx, scalarSquareMatrix &dfdy) const =0
Calculate the Jacobian of the system.
static void resizeField(UList< Type > &f, const label n)
Definition: ODESolverI.H:48
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.
label n_
Size of the ODESystem (adjustable)
Definition: ODESolver.H:64
Namespace for OpenFOAM.
void LUBacksubstitute(const scalarSquareMatrix &luMmatrix, const labelList &pivotIndices, List< Type > &source)
LU back-substitution with given source, returning the solution.