54efbaa320
CanteraError inerits from std:exception, so now it has a what() method that is used to print a message describing the exception. Adding an exception to the Cantera error stack now requires explicitly calling the .save() method.
129 lines
3.5 KiB
C++
129 lines
3.5 KiB
C++
/// @file blasius.cpp
|
|
/// The Blasius boundary layer
|
|
|
|
#include <cantera/Cantera.h>
|
|
#include "BoundaryValueProblem.h"
|
|
|
|
|
|
/**
|
|
* This class solves the Blasius boundary value problem on the domain (0,L):
|
|
* \f[
|
|
* \frac{d\zeta}{dz} = u.
|
|
* \f]
|
|
* \f[
|
|
* \frac{d^2u}{dz^2} + 0.5\zeta \frac{du}{dz} = 0.
|
|
* \f]
|
|
* with boundary conditions
|
|
* \f[
|
|
* \zeta(0) = 0, u(0) = 0, u(L) = 1.
|
|
* \f]
|
|
* Note that this is formulated as a system of two equations, with maximum
|
|
* order of 2, rather than as a single third-order boundary value problem.
|
|
* For reasons having to do with the band structure of the Jacobian, no
|
|
* equation in the system should have order greater than 2.
|
|
*/
|
|
class Blasius : public BVP::BoundaryValueProblem
|
|
{
|
|
|
|
public:
|
|
|
|
// This problem has two components (zeta and u)
|
|
Blasius(int np, double L) : BVP::BoundaryValueProblem(2, np, 0.0, L) {
|
|
|
|
// specify the component bounds, error tolerances, and names.
|
|
BVP::Component A;
|
|
A.lower = -200.0;
|
|
A.upper = 200.0;
|
|
A.rtol = 1.0e-12;
|
|
A.atol = 1.0e-15;
|
|
A.name = "zeta";
|
|
setComponent(0, A); // zeta will be component 0
|
|
|
|
BVP::Component B;
|
|
B.lower = -200.0;
|
|
B.upper = 200.0;
|
|
B.rtol = 1.0e-12;
|
|
B.atol = 1.0e-15;
|
|
B.name = "u";
|
|
setComponent(1, B); // u will be component 1
|
|
}
|
|
|
|
|
|
// destructor
|
|
virtual ~Blasius() {}
|
|
|
|
// specify guesses for the initial values. These can be anything
|
|
// that leads to a converged solution.
|
|
virtual doublereal initialValue(int n, int j) {
|
|
switch (n) {
|
|
case 0:
|
|
return 0.1*z(j);
|
|
case 1:
|
|
return 0.5*z(j);
|
|
default:
|
|
return 0.0;
|
|
}
|
|
}
|
|
|
|
// Specify the residual. This is where the ODE system and boundary
|
|
// conditions are specified. The solver will attempt to find a solution
|
|
// x so that this function returns 0 for all n and j.
|
|
virtual doublereal residual(doublereal* x, size_t n, size_t j) {
|
|
|
|
// if n = 0, return the residual for the first ODE
|
|
if (n == 0) {
|
|
if (isLeft(j)) { // here we specify zeta(0) = 0
|
|
return zeta(x,j);
|
|
} else
|
|
// this implements d(zeta)/dz = u
|
|
{
|
|
return (zeta(x,j) - zeta(x,j-1))/(z(j)-z(j-1)) - u(x,j);
|
|
}
|
|
}
|
|
// if n = 1, then return the residual for the second ODE
|
|
else {
|
|
if (isLeft(j)) { // here we specify u(0) = 0
|
|
return u(x,j);
|
|
} else if (isRight(j)) { // and here we specify u(L) = 1
|
|
return u(x,j) - 1.0;
|
|
} else
|
|
// this implements the 2nd ODE
|
|
{
|
|
return cdif2(x,1,j) + 0.5*zeta(x,j)*centralFirstDeriv(x,1,j);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
private:
|
|
|
|
// for convenience only. Note that the compiler will inline these.
|
|
double zeta(double* x, int j) {
|
|
return value(x,0,j);
|
|
}
|
|
double u(double* x, int j) {
|
|
return value(x,1,j);
|
|
}
|
|
|
|
};
|
|
|
|
|
|
int main()
|
|
{
|
|
try {
|
|
|
|
// Specify a problem on (0,10), with an initial uniform grid of
|
|
// 6 points.
|
|
Blasius eqs(6, 10.0);
|
|
// Solve the equations, refining the grid as needed, and print lots of diagnostic output (loglevel = 4)
|
|
eqs.solve(4);
|
|
// write the solution to a CSV file.
|
|
eqs.writeCSV();
|
|
return 0;
|
|
} catch (Cantera::CanteraError& err) {
|
|
std::cerr << err.what() << std::endl;
|
|
return -1;
|
|
}
|
|
}
|
|
|
|
|