Characters with the same sound as "Yu" and belonging to the Fire Element in Chinese mythology and philosophy are primarily associated with the Chinese zodiac and the Five Elements theory. The character "Yu" sounds similar to the Chinese character for "猪" (zhū), which represents the pig in the zodiac cycle. In the context of the Fire Element, the following characters are relevant:

1. 猪 (zhū): The pig is the twelfth and final animal in the Chinese zodiac, symbolizing prosperity and happiness. It is associated with the Fire Element, particularly in the context of the Chinese zodiac's Five Elements cycle.

2. 鱼 (yú): The fish is another character that sounds similar to "Yu" and is associated with the Water Element, which is complementary to Fire in the Five Elements theory. However, it is not a direct match for the Fire Element.

3. 雨 (yǔ): Rain, represented by the character "雨," is associated with the Water Element, which is the polar opposite of Fire. Therefore, it does not belong to the Fire Element.

The association of characters with the Fire Element is rooted in the ancient Chinese philosophical system known as the Five Elements, which are Wood, Fire, Earth, Metal, and Water. Each element is believed to be associated with certain characteristics, seasons, and animals. The Fire Element is associated with summer, warmth, and passion, and is often represented by the colors red and orange.

The character "猪" (zhū) is particularly relevant because it is the only character that both sounds like "Yu" and is directly associated with the Fire Element in the context of the Chinese zodiac. This association is not arbitrary; it is based on the cyclical nature of the Chinese zodiac and the Five Elements theory. The zodiac cycle repeats every 12 years, and each year is associated with one of the 12 animals, each of which is further associated with one of the Five Elements. The pig, as the twelfth animal, is thus associated with the Fire Element.

In conclusion, the character "猪" (zhū) is the primary character that has the same sound as "Yu" and belongs to the Fire Element in the context of Chinese mythology and philosophy. This association is based on the Chinese zodiac and the Five Elements theory, which are deeply ingrained in Chinese culture and thought.