Enhanced solar steam generation is a promising process for water purification. Evaporation efficiency can be increased by localizing heating process at the water-air interface using photothermal materials. As of late, numerous black absorber sheets (BAS) have been developed, which can be seen as meta-foams with micro/nanostructured porous media exhibiting remarkable properties in terms of solar radiation-to-heat conversion to achieve efficient steam generation. By taking advantage of the porous structure of the BAS, both thermal insulation and stable water capillary transport functions are simultaneously achieved by the same material. Water heating is therefore concentrated only at the surface, which increases the evaporation efficiency up to 85% under 1 sun illumination. In this contribution, we report on theoretical modeling and numerical simulations of BAS-assisted steam generation to guide the optimization of BAS regarding the maximization of the evaporation rate. Numerical simulations are performed using multi-physical simulation tools to simultaneously account for heat and mass transfer including photo-thermal conversion, capillary transport and water phase change. Parametric studies are also conducted to determine the key parameters for an optimized BAS maximizing steam generation rate. Considered parameters include the porosity ε and the surface absorptivity α of BAS. An optimal porosity of 0.75 is found to maximize the evaporation rate. We also report on the observed trend of the evaporation rate with respect to key parameters of the BAS structure.