Direct Numerical Simulation (DNS) of hydrodynamics and mass transfer in bubbles in the wobbling regime is reported using the Unstructured Conservative Level Set (UCLS) method. The finite-volume method on 3D collocated unstructured meshes discretizes the transport equations. The fractional-step projection method solves the pressure-velocity coupling in the momentum equation. Unstructured flux limiter schemes discretize the convective term of transport equations to minimize the numerical diffusion and avoid numerical oscillations in regions with strong gradients. The combination of these numerical schemes proves to keep the numerical stability of bubbles in the wobbling regime, that is, high Reynolds and Eötvös numbers. Numerical and physical findings on the hydrodynamics and mass transfer in wobbling bubbles are reported.