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Does it simply ignore the previous goal and recomputes the optimal trajectory for the newest goal?

This is what will happen if you continuously send goals. The move_base simple action server will receive the new goal, send it to the global planner to generate your global plan, and then the global plan is passed off to the local planner for path following / obstacle avoidance etc. If you're looking for more flexibility in your navigation strategy, you should check out the move_base_flex package.