A numerical tool is developed to help design magnetohydrodynamics power-generation panels to be used onboard a reentry vehicle. The tool consists of two parts: a magnetohydrodynamics flow solver and a Poisson solver. The magnetohydrodynamics flow solver deals with the two-dimensional Navier-Stokes equations extended to incorporate magnetohydrodynamics effects and chemical reactions. The Poisson equation for the electric potential is discretized with a 19-point stencil in three-dimensional space. The Poisson solver is tested with three cases, and all the results reproduce the analytical solutions and those from the literature. Then it is used to compute the electric field, current-density distributions, and total power generation around a reentry vehicle with onboard electrodes. We compare the results with the previous two-dimensional simulation results. Several three-dimensional plots of the current stream traces are presented, and from the plots the current is categorized into five types. The net current through each electrode surface and the corresponding power extraction are computed. At the present stage, the magnetohydrodynamics Poisson solver is uncoupled from the flow solver.