These discretizations need to be extended for general case which is not U itself but rather a function of U and its partial derivatives |
All the derivatives need to be modified near boundaries where some of needed points are missing |
NAS also adds a new numerical dissipation term to improve stability of numerical solution. Previously highest order derivative came from viscous terms like Ñ2U. |
New term is proportional to Ñ4U |
Note the negative sign which gives dissipation i.e. stability |
Equations (3.25) (3.26) and (3.27) summarize the equations after spatial and temporal discreization |