Hollie, substantiation has nothing to do with the OP. The post is hypothetical. If there was a flood, and no blacks or Asians were on board.........
There is no way to tell whether or not those two ethnic groups were or were not on board except for the information we are given in the Bible.
If there was a flood, and the story is true, then this answers the question.
A point was made as to the skin color of Noah's children. Shem means "dusky". Japheth means "fair", Ham means "to be black".
Here is where their children settled according to the Bible:
Ham's children went to = Ethiopia, Egypt, Libya, Canaan, among others.
Shem's children settled in = Arabia, Syria, among others.
And these are the routes mapped out that Japheth's 7 son's took:
1. Javan (Greece, Romans, Romance -- French, Italians, Spanish, Portuguese)
2. Magog (Scythians, Slavs, Russians, Bulgarians, Bohemians, Poles, Slovaks, Croatians)
3. Madai (Indians & Iranic: Medes, Persians, Afghans, Kurds)
4. Tubal (South of Black Sea)
5. Tiras (Thracians, Teutons, Germans, Scandinavian, Anglo-Saxon, Jutes)
6. Meshech (Russia)
7. Gomer (Celtic)
If the flood happened, there is your answer.