Fiber tractography is useful for studying a variety of biological phenomena associated with transversely isotropic tissues, in which fibers serve to provide functional strength along a specific axis. One useful application of fiber tractography is finite-element analysis (FEA) studies. Here, we present a method utilizing computational fluid dynamics (CFD) for efficiently determining fiber trajectories in a transversely isotropic material with arbitrary structures of any complexity (such as those determined from biomedical imaging). We demonstrate assignment of fiber directions to FEA mesh by registration with the CFD mesh. Sensitivity analysis on various solver settings, flow characteristics, and material parameters shows less than 2 degrees of average deviation from the nominal fiber vectors if the Reynolds number is <1 and the flow is laminar and incompressible with our nominal fluid properties (viscosity of 1Pa-s and density of 1g/cm^3). Flow guides can be used to help correct fiber trajectories to experimental or anatomical observations, such as twisting in the Achilles tendon. This method also provides an elegant solution to determining fiber tracts in muscles that intertwine with each other, such as in the soft palate complex. For FEA studies, this method enables efficient determination and assignment of fiber directions to any finite-element mesh.