[optimux]

Originally Posted by unogamerules

Yes, I derived continuity equation by myself from mass conservation, but failed for the momentum equations. There must be something missing that I have to dig into.

You have to first derive all operators in spherical coordinates and apply them onto field variables. Then you may have a chance.

[Slyphlamen]

Had some identical trouble when dealing with my model, where I use compressible Euler; but I think for NS equations you'll find more litterature than on specifically Euler.


A nice place if you derive everything yourself https://mathworld.wolfram.com/SphericalCoordinates.html ; but you can definitely find the NS given in an article (although you might find continuity, momentum, and energy es given separatly as they are long to write). From a quick search typically I found this https://www.google.com/url?sa=t&rct=...zL_IF0JoBM-8wK


Physically speaking, moving from Cartesian to curvilinear geometries (such as spherical coordinates) adds a curvature term to your equations from what I understood (at least in the compressible Euler case; but I wouldn't be surprised if this can be extended to NS).

[optimux]

Originally Posted by Slyphlamen

Had some identical trouble when dealing with my model, where I use compressible Euler; but I think for NS equations you'll find more litterature than on specifically Euler.


A nice place if you derive everything yourself https://mathworld.wolfram.com/SphericalCoordinates.html ; but you can definitely find the NS given in an article (although you might find continuity, momentum, and energy es given separatly as they are long to write). From a quick search typically I found this https://www.google.com/url?sa=t&rct=...zL_IF0JoBM-8wK


Physically speaking, moving from Cartesian to curvilinear geometries (such as spherical coordinates) adds a curvature term to your equations from what I understood (at least in the compressible Euler case; but I wouldn't be surprised if this can be extended to NS).

Yeah, that MMA page is pretty useful. Thank you so much.

[Slyphlamen]

Originally Posted by optimux

Yeah, that MMA page is pretty useful. Thank you so much.

Another cool article that helped me a lot understand how things worked is the first article of the Zeus-2D code. For you specifically you might want to check Appendix A of https://ui.adsabs.harvard.edu/abs/1992ApJS...80..753S


The code is in Fortran but it's avalaible online https://www.astro.princeton.edu/~jstone/zeus.html


Again this is for compressible Euler and not NS; but there are many similarities obviously.

[optimux]

Originally Posted by Slyphlamen

Another cool article that helped me a lot understand how things worked is the first article of the Zeus-2D code. For you specifically you might want to check Appendix A of https://ui.adsabs.harvard.edu/abs/1992ApJS...80..753S


The code is in Fortran but it's avalaible online https://www.astro.princeton.edu/~jstone/zeus.html


Again this is for compressible Euler and not NS; but there are many similarities obviously.

Also, a paper from Santelli, Luca "A finite–difference scheme for three–dimensional incompressible flows in spherical coordinates" is helpful. Now I'm using spectral method for High Ra number (of course incompressible flow). Thank you so much for your papers and codes.

Cheers!