Nitei Gavriel (Hilchot Yom Tov, volume 1, chapter 21, paragraph 4) says:
ד. מותר לשים ביו״ט קדירה של מים ע״ג האש כדי שיעברו על
שפת הקדירה ויכבו את האש מתחתיו, אכן יש לו להשתמש במים
לבישול קדירה וכדומה דהו״ל לצורך יו״ט, ודוקא במקום צורך כגון
שמפחד שהילדים יתקרבו להאש, אז מותר למלאות קדירה מים, כדי
להרתיח על האש לצורך שתיה, בכוונה שהמים בשעת רתיחתם ישפכו
לחוץ ויכבו האש
ה. ואם נכבה מותר לסגור את הכפתור של הגאז שלא ימשיך
לזרום גאז משום חשש סכנה , ונכון לסגרו בשינוי אם אפשר
My translation:
On Yom Tov, one is permitted to place a pot of water on the fire in order that the water overflow and extinguish the fire underneath it. He should however, use the water for cooking or the like, so that the boiling of the water was for a Yom Tov need.
Specifically where there is a need to do so, such as if one is scared the children will come close to the fire, one is permitted to fill a pot with water and place it on the fire in order that the water is heated for drinking purposes, with the intention that when the water will boil it will overflow and put out the fire.
Because of the possible danger, if the fire is extinguished one is permitted to turn off the gas so that the gass won't leak. If possible, it is preferable to turn the knob with a Shinui (using a non-standard action).
In the footnotes, he explains (based on Shulchan Aruch Orach Chaim 514:3 and the commentaries there) that causing something to be extinguished is only forbidden if you are touching the lit thing, but if you indirectly cause the extinguishing, it is not a problem. Here you are not touching the fire, rather you are touching the pot, and the fire itself causes the water to overflow and extinguish itself.
See Shulchan Aruch Orach Chaim 514:3 and the Mishna Berura there, especially S"K 19.
Shulchan Aruch Harav (514:9 and Kuntres Acharon 514:3) says that one should only indirectly extinguish a fire when there is a great need.
With regards to placing a candle where the wind might blow it out, The Remah at the end of 514:3 says that one is permitted to put a candle where the wind might blow it out, as long as the wind is not blowing, but if the wind is blowing it is forbidden. The Mishna Berurah (S"K 25) says that there are Achronim (the Magen Avaham) who are strict and say that even when the wind is not blowing one should not put the candle there, since the wind blows every second. In the Biur Halacha the Mishna Berurah agrees with these Achronim. The Shulchan Aruch HaRav (514:10) is one of those Achronim who say one should not do it even when the wind is not blowing