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Droplet impact and breakup on meshes are relevant to a number of applications involving filters, textiles, and other spatially inhomogeneous media encountering gas-dispersed liquids. This study presents high-resolution simulation results of mm-size droplets striking wettability-patterned meshes with the goal of (a) replicating prior physical experiments, (b) identifying sensitivities to the initial conditions and wettability of the mesh wires, and (c) studying the fluid-field dynamics when droplets strike such meshes. The insights from the present model may help to advance understanding of droplet atomization on meshes, which depends on a number of parameters that are nontrivial to control in an experimental setting. The analysis is carried out by benchmarking the numerical methods used in a commercial software package for orthogonal droplet impact on a flat smooth surface, followed by a convergence analysis, and finally, simulation of specific experiments and case studies involving wettability-patterned mesh targets. We show that the wettability contrast between the hydrophilic and hydrophobic domains on the mesh as well as the contact angle hysteresis on each side play a critical role in determining whether liquid pinch-off occurs. The three-dimensional computational framework constructed in this work is a step toward predicting the postimpact behavior of droplets that strike woven meshes and other porous inhomogeneous media consisting of materials with different wetting properties.