How can I calculate when the new moon will be observed from a particular meridian?
You need an Orrery. Specifically, one that includes Earth’s rotation.

My noting the meridian on the model Earth, you can see how the Earth may be rotated some amount each time the Moon passes on a line between the Earth and Sun.

The wikipedia page gives a formula.  Take the result (given in UT) and apply the timezone offset for the desired longitude.

The same page discusses Lunar calindars and may have the info you are really interested in.