The gas-jet wiping process is an industrial coating technique aiming to control the final coating thickness on a steel strip. This process comes with imperfections such as a non-uniform coating due to several phenomena and could gain a lot from an accurate numerical simulation. This process is particularly challenging to simulate numerically because it involves a localized turbulent air flow impacting a very thin liquid film showing a high surface tension coefficient. Moreover, the scale variations are extreme: from meter to micrometer in space and one to hundred microsecond time. Due to the nature of the process problems, simulations must be in 3D. Related works in literature only achieve simulations limited to 2D or with parameters far from actual industrial applications. This work aims to simulate the wiping process by using an academic software based on stabilized finite elements, immersed methods (convected level-set) and a fully monolithic framework with anisotropic metric-based mesh adaptation. Our first results are concerned with the two stages involved in the process, and aims to validate in a separate way, the dragout simulation and the impinging jet calculation with comparisons with experimental data. We present our results on these problems in 2D and their extension to 3D. We studied the final film thickness for the dragout and the velocity and pressure fields for the impinging jet. We compare them with results from the literature or experimental data. We also show our results at attempting the complete wiping process.