Characterized by complex geometry and complicated dynamic process, biological fluid dynamics in swimming and flying is usually of large scale vortex flows with four-dimensional nature, namely, spatial three-dimensional and one-dimensional in time. Conventional theories for understanding power and energetics in swimming and flying rely exclusively on the consistent potential flow formulation in qualitatively analyzing the physics as well as the observations and measurements in visualizing the flows so as to support the theories. In the present paper we address a new paradigm of the so-called, simulation-based biological fluid dynamics that can digitize and visualize swimming and flying by using computational mechanical modeling of the biological fluid dynamics through faithful reconstruction of morphology and realistic representation of kinematics of an individual object. We demonstrate an integrated computational system as a baseline for the simulation-based biological fluid dynamics, which involves four subsystems of the morphological modeling, the kinematic modeling, the computational fluid dynamic modeling, and the post-processing for visualization. Applications of a realistic model of insect flapping flight and an extensive study on the Micro Air Vehicle are then presented and discussed.