All the instances of schemes are (and has to be) created with the procedure fd_initialize()
Schemes are used to directly or indirectly build FD schemes:
scheme_builder_non_uniform
interface. To do so, simply write a function that simply:fd_scheme%declare_stencil
member routine)fd_scheme%stencilweight
arrayfd_scheme
Derivative | Order | Type | Name | Definition |
---|---|---|---|---|
First | 1 | Backward | t_fd_scheme_first_o1_backward | \( \frac{\phi_{i}-\phi_{i-1}}{\Delta x} \) |
First | 1 | Forward | t_fd_scheme_first_o1_forward | \( \frac{\phi_{i-1}-\phi_{i}}{\Delta x} \) |
First | 2 | Backward | t_fd_scheme_first_o2_backward | \( \frac{\phi_{i-2}-4\phi_{i-1}+3\phi_{i}}{2 \Delta x} \) |
First | 2 | Centered | fd_scheme_first_o2_centered | \( \frac{\phi_{i+1}-\phi_{i-1}}{2 \Delta x} \) |
First | 2 | Forward | t_fd_scheme_first_o2_forward | \( \frac{-\phi_{i+2}+4\phi_{i+1}-3\phi_{i}}{2 \Delta x} \) |
Second | 2 | Centered | fd_scheme_second_o2_centered | \( \frac{\phi_{i+1}-2\phi_{i}+\phi_{i-1}}{\Delta x^2} \) |