Recent experimental and modeling studies show that large quasi-static electric fields (2--20 kV/m) can be developed in a Martian or terrestrial dust devil as a result of contact electrification and charge separation of dust grains with different sizes and compositions. Electric discharging occurs when the maximum electric field reaches breakdown values (~20 kV/m on Mars and ~3 MV/m on Earth, at surface altitudes). We derive a maximum electric field in a dust devil and develop a two-dimensional (2-D) cylindrically symmetric finite element model for Martian and terrestrial dust devil simulations. Unlike previous models with unlimited field growth, the tribocharging process and the time evolution of the dust devil electric field are self-consistently limited in our model and the saturated maximum electric fields in our simulations are comparable to past measurements. We study the saturated maximum electric fields for dust storms of different size, atmosphere conductivity and time rate of tribocharging. We also discuss the 2-D cylindrical field structures surrounding a dust devil and the conductivity gradient effect to the field growth of large Martian dust storms.