Can I keep a cooking fire going by adding logs to it on Yom Tov?
Yes, you may.
I would like to point out that there are several other halachos involved in cooking on wood over yom tov that you should be aware of:
- One may not use firewood for any other purpose than burning, as it is muktzeh.
- On yom tov one cannot make a layered pile of wood to burn unless one holds the upper layer suspended in the air while the lower layer is being placed under it.
- One cannot take a log that has already (partially) caught fire out of the general fire, and if one wants to change the placement of the burning log in the fire one should do so without completely removing it from the general fire.
שו”ע אדה”ז סי’ תק”ב.