Kanji is a written language of expressing meaning , “会” has a meaning of meeting to someone,”合” has a meaning of doing something with some.合う、会う、逢う、遭う、遇う　have same pronounce,but different kanji has different meaning.by the way ,these kanji could express meeting,just difference of situation .

In my perspective, 合う is matching to something and 会う(逢う,遭う) is physically meeting with people :) Also original meaning of the words or comes from what Ueda-san described earlier :))

I think so. If you just know the common essence of those words, you can easily guess what each and every word means in a particular context. ／会う, 合う, 逢う（"go on a date with someone" as in "逢引"）, 遇う（"happen to meet" as in "奇遇"）, 遭う（"meet with a disaster", as in "遭難"）, etc.

I see, so they are different but essentially mean the same thing.

Just to let you know a bit more, there are some other "あう" written differently in kanji, such as "逢う", "遇う", and "遭う", all of which fundamentally mean "get together".