fdm module
Module Finite Difference Method describe derivatives used in numerical method (FDM)
Note
The file contains a set of procedures allowing calculations using the finite difference method in cylindrical space (2D) temperature change at any point in time. The procedures were derived for an asymmetric mesh.
t[n] - temperature in node n, d[n] - distance in the coordinates Z and R, between node 4 and node n,
a(k) - temperature equalization factor [m^2/s] for material k
t[0] Z ^
O |
| (0) |
(3) |d[0] |
| 0----------> R
t[3] O------t[4]-----------O t[1]
d[3] | d[1]
| (1)
(2) | d[2]
|
O
t[2]
- fdm.d2tdr2(t, dx, a)[source]
Second derivative of temperature by radius
- Parameters:
t – temperature vector [°C]
dx – distance from the central node [m]
a – temperature equalization factor vector [m^2/s]
- Returns:
second derivative of temperature by radius
- fdm.d2tdz2(t, dx, a, r)[source]
Second derivative of temperature by depth
- Parameters:
t – temperature vector [°C]
dx – distance from the central node [m]
a – temperature equalization factor vector [m^2/s]
r – radius counted from the axis of symmetry [m]
- Returns:
Second derivative of temperature by depth
- fdm.dtdr(t, dx, a, r)[source]
First derivative of temperature by radius
- Parameters:
t – temperature vector [°C]
dx – distance from the central node [m]
a – temperature equalization factor vector [m^2/s]
r – radius counted from the axis of symmetry [m]
- Returns:
first derivative of temperature by radius