[Nam Tran Ha]

Hello everybody.
I'm writing a CFD code for supersonic flow over a delta wing. In my project, the governing equations is in term of a generalized nonorthogonal curvilinear coordinate system (equation 1 in the the attachment). But the formula of MacCormack & Baldwin artificial viscosity i found in many references (equation 2 and 3 in the attachment) is in term of cartesian coordinate system. How can i add this artificial viscosity in my governing equations. The method i used is Explicit MacCormack Method.

I added the original formula of artificial viscosity (in term of Cartesian coordinate system) in the original governing equations (in term of Cartesian coordinate system too) and tried transforming it to generalized nonorthogonal curvilinear coordinate system, but i didn't know how to deal with (delta x)^4.

Sorry for my bad english.
Thanks in adcance.