- #1
mertcan
- 340
- 6
Hi, first of all I am aware of the fact that QUICK SCHEME used in computational fluid dynamics has consistent slope at the sides of node elements (for instance at the left side of node 3 in my attachment same slopes exist) as you can see in my picture/attachment. But I must express that I can prove (differentiating the second order interpolation polynom at side point of nodes) slopes at the left side of node(like in picture) are equal in QUICK SCHEME thus it is consistent but I know there are another schemes like VAN LEER or VAN ALBADA SCHEME which are non linear and I can NOT prove how those SCHEMES may be consistent in terms of slope at the left side of node like QUICK SCHEME. At the centre of length (length between node 2 and node 3 in my attachment) which means left side of node 3 QUICK SCHEME always ensure the consistency of slope and I can prove but HOW DO WE KNOW THAT VAN LEER VAN ALBADA SCHEMES MAY ENSURE THE CONSISTENCY OF slope at the left side of node 3?? How can we PROVE it?
For instance in order to prove QUICK SCHEME is consistent in terms of slope at the left point of node element I can use the continuous second order polynomial interpolation and differentiate it. BUT in VAN LEER or VAN ALBADA SCHEME I do not know the continuous form of polynomial interpolation thus I can not differentiate like in the case of QUICK SCHEME...
For instance in order to prove QUICK SCHEME is consistent in terms of slope at the left point of node element I can use the continuous second order polynomial interpolation and differentiate it. BUT in VAN LEER or VAN ALBADA SCHEME I do not know the continuous form of polynomial interpolation thus I can not differentiate like in the case of QUICK SCHEME...