Acoustic radiation force trapping is widely used for particle manipulation in both gases and liquids. Simple standing wave fields have traditionally been employed, but developments in ultrasound wave field control have shifted focus towards single-point traps, specifically acoustic vortices. These fields carry orbital angular momentum, inducing rotational motion of the particles around the vortex axis. While such fields can enhance particle manipulation capabilities, the rotational motion can lead to instability in particle positioning or cause particle ejection, posing challenges for high-precision applications. We developed a finite element method model for simulating Rayleigh-regime particle dynamics in arbitrary acoustic fields, simulating the effect of acoustic radiation force and acoustic streaming. The acoustic pressure fields and fluid flow patterns are simulated for several single-point traps. Particle trapping ability is characterized as functions of particle properties and acoustic pressure. The simulation can estimate the suitable acoustic parameters for stable trapping of a variety of particles, enabling trapping optimization for specific applications.