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Factor out root of cubic to be used also for update_gradient

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We can use the analytic solution of a cubic in two different places.

Signed-off-by: Robert C. Helling <helling@atdotde.de>
Signed-off-by: Dirk Hohndel <dirk@hohndel.org>
This commit is contained in:
Robert C. Helling 2015-08-17 21:36:50 +02:00 • committed by Dirk Hohndel
parent d93984448c
commit 930e83dfc4
1 changed files with 27 additions and 29 deletions
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56
deco.c
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@ -316,26 +316,37 @@ void vpmb_next_gradient(double deco_time, double surface_pressure)
}
}
// A*r^3 - B*r^2 - C == 0
// Solved with the help of mathematica
#define cube(x) (x * x * x)
double solve_cubic(double A, double B, double C)
{
double BA = B/A;
double CA = C/A;
double discriminant = CA * (4 * cube(BA) + 27 * CA);
// Let's make sure we have a real solution:
if (discriminant < 0.0) {
// This should better not happen
report_error("Complex solution for inner pressure encountered!\n A=%f\tB=%f\tC=%f\n", A, B, C);
return 0.0;
}
double denominator = pow(cube(BA) + 1.5 * (9 * CA + sqrt(3.0) * sqrt(discriminant)), 1/3.0);
return (BA + BA * BA / denominator + denominator) / 3.0;
}
double update_gradient(double first_stop_pressure, double next_stop_pressure, double first_gradient)
{
double first_radius = 2.0 * vpmb_config.surface_tension_gamma / first_gradient;
double A = next_stop_pressure;
double B = -2.0 * vpmb_config.surface_tension_gamma;
double C = (first_stop_pressure + 2.0 * vpmb_config.surface_tension_gamma / first_radius) * pow(first_radius, 3.0);
double C = (first_stop_pressure + 2.0 * vpmb_config.surface_tension_gamma / first_radius) * cube(first_radius);
double next_radius = solve_cubic(A, B, C);
double low = first_radius;
double high = first_radius * pow(first_stop_pressure / next_stop_pressure, (1.0/3.0));
double next_radius;
double value;
int ci;
for (ci = 0; ci < 100; ++ci){
next_radius = (high + low) /2.0;
value = A * pow(next_radius, 3.0) - B * next_radius * next_radius - C;
if (value < 0)
low = next_radius;
else
high = next_radius;
}
return 2.0 * vpmb_config.surface_tension_gamma / next_radius;
}
@ -365,31 +376,18 @@ void nuclear_regeneration(double time)
}
}
// Calculates the nucleons inner pressure during the impermeable period
double calc_inner_pressure(double crit_radius, double onset_tension, double current_ambient_pressure)
{
double onset_radius = 1.0 / (vpmb_config.gradient_of_imperm / (2.0 * (vpmb_config.skin_compression_gammaC - vpmb_config.surface_tension_gamma)) + 1.0 / crit_radius);
// A*r^3 + B*r^2 + C == 0
// Solved with the help of mathematica
double A = current_ambient_pressure - vpmb_config.gradient_of_imperm + (2.0 * (vpmb_config.skin_compression_gammaC - vpmb_config.surface_tension_gamma)) / onset_radius;
double B = 2.0 * (vpmb_config.skin_compression_gammaC - vpmb_config.surface_tension_gamma);
double C = onset_tension * pow(onset_radius, 3);
double BA = B/A;
double CA = C/A;
double discriminant = CA * (4 * BA * BA * BA + 27 * CA);
// Let's make sure we have a real solution:
if (discriminant < 0.0) {
// This should better not happen
report_error("Complex solution for inner pressure encountered!\n A=%f\tB=%f\tC=%f\n", A, B, C);
return 0.0;
}
double denominator = pow(BA * BA * BA + 1.5 * (9 * CA + sqrt(3.0) * sqrt(discriminant)), 1/3.0);
double current_radius = (BA + BA * BA / denominator + denominator) / 3.0;
double current_radius = solve_cubic(A, B, C);
return onset_tension * onset_radius * onset_radius * onset_radius / (current_radius * current_radius * current_radius);
}