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ODESolvers/RKF45: Error evaluation is now consistent with the other RK solvers

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This commit is contained in:
Henry 2013-11-03 16:03:03 +00:00
parent 277d153bef
commit b1c955337f
2 changed files with 22 additions and 26 deletions
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28
src/ODE/ODESolvers/RKF45/RKF45.C
View File

@ -56,19 +56,17 @@ const scalar
RKF45::a64 = 1859.0/4104.0,
RKF45::a65 = -11.0/40.0,
RKF45::b41 = 25.0/216.0,
RKF45::b42 = 0.0,
RKF45::b43 = 1408.0/2565.0,
RKF45::b44 = 2197.0/4104.0,
RKF45::b45 = -1.0/5.0,
RKF45::b46 = 0.0,
RKF45::b1 = 16.0/135.0,
RKF45::b3 = 6656.0/12825.0,
RKF45::b4 = 28561.0/56430.0,
RKF45::b5 = -9.0/50.0,
RKF45::b6 = 2.0/55.0,
RKF45::b51 = 16.0/135.0,
RKF45::b52 = 0.0,
RKF45::b53 = 6656.0/12825.0,
RKF45::b54 = 28561.0/56430.0,
RKF45::b55 = -9.0/50.0,
RKF45::b56 = 2.0/55.0;
RKF45::e1 = 25.0/216.0 - RKF45::b1,
RKF45::e3 = 1408.0/2565.0 - RKF45::b3,
RKF45::e4 = 2197.0/4104.0 - RKF45::b4,
RKF45::e5 = -1.0/5.0 - RKF45::b5,
RKF45::e6 = -RKF45::b6;
}
@ -143,7 +141,7 @@ Foam::scalar Foam::RKF45::solve
{
y[i] = y0[i]
+ dx
*(b51*dydx0[i] + b53*k3_[i] + b54*k4_[i] + b55*k5_[i] + b56*k6_[i]);
*(b1*dydx0[i] + b3*k3_[i] + b4*k4_[i] + b5*k5_[i] + b6*k6_[i]);
}
// Calculate the error estimate from the difference between the
@ -152,9 +150,7 @@ Foam::scalar Foam::RKF45::solve
{
err_[i] =
dx
*(b41*dydx0[i] + b43*k3_[i] + b44*k4_[i] + b45*k5_[i])
- (y[i] - y0[i])
;
*(e1*dydx0[i] + e3*k3_[i] + e4*k4_[i] + e5*k5_[i] + e6*k6_[i]);
}
return normalizeError(y0, y, err_);

20
src/ODE/ODESolvers/RKF45/RKF45.H
View File

@ -31,15 +31,15 @@ Description
\verbatim
"Low-order classical Runge-Kutta formulas with step size control
and their application to some heat transfer problems."
Fehlberg, E.,
NASA Technical Report 315 1969
Fehlberg, E.,
NASA Technical Report 315, 1969.
"Solving Ordinary Differential Equations I: Nonstiff Problems,
second edition",
Hairer, E.,
Nørsett, S.,
Wanner, G.,
Springer-Verlag, Berlin. 1993, ISBN 3-540-56670-8.
"Solving Ordinary Differential Equations I: Nonstiff Problems,
second edition",
Hairer, E.,
Nørsett, S.,
Wanner, G.,
Springer-Verlag, Berlin. 1993, ISBN 3-540-56670-8.
\endverbatim
This method embedds the 4-th order integration step into the 5-th order step
@ -112,8 +112,8 @@ class RKF45
c2, c3, c4, c5, c6,
a21, a31, a32, a41, a42, a43, a51, a52, a53, a54,
a61, a62, a63, a64, a65,
b41, b42, b43, b44, b45, b46,
b51, b52, b53, b54, b55, b56;
b1, b3, b4, b5, b6,
e1, e3, e4, e5, e6;
// Temporary fields