Analytical Class Reference

Analytical solution for the 1D heat equation. More...

#include <analytical.hpp>

Collaboration diagram for Analytical:

Static Public Member Functions
static double	solve (double t, double x, const PhysParams &phys)
	Compute the exact temperature at a given time and position.
static std::vector< double >	get_profile (double t, const std::vector< double > &x_grid, const PhysParams &phys)
	Generate a full temperature profile for a set of grid points.

Detailed Description

Analytical solution for the 1D heat equation.

Problem: dT/dt = D * d^2T/dx^2 IC: T(x, 0) = Tin BC: T(0, t) = T(L, t) = Tsur

Solution (Series expansion): T(x,t) = Tsur + (Tin - Tsur) * 4/pi * Sum_{k=0,1,...} [ 1/(2k+1) * sin((2k+1)*pi*x/L) * exp(-D*((2k+1)*pi/L)^2 * t) ]

Definition at line 18 of file analytical.hpp.

Member Function Documentation

get_profile()

std::vector< double > Analytical::get_profile ( double t, const std::vector< double > & x_grid, const PhysParams & phys )

static

Generate a full temperature profile for a set of grid points.

Parameters

t	Time [h]
x_grid	Vector of positions
phys	Physical parameters

Returns

Vector of temperatures corresponding to x_grid

Definition at line 37 of file analytical.cpp.

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solve()

double Analytical::solve ( double t, double x, const PhysParams & phys )

static

Compute the exact temperature at a given time and position.

Parameters

t	Time [h]
x	Position [cm]
phys	Physical parameters (L, D, Tin, Tsur)

Returns

Temperature [°C]

Definition at line 6 of file analytical.cpp.

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The documentation for this class was generated from the following files:

• include/methods/analytical.hpp
• src/methods/analytical.cpp