Application of two- and-three dimensional computational fluid dynamics (2D and 3D CFD) models to subsonic flowing-gas DPALs is reported. The 2D model is applied to a DPAL with optical resonator-flow field coaxial configuration and the 3D model is applied to an optical axis transverse to the flow configuration. The models take into account effects of temperature rise and losses of alkali atoms due to ionization. The 2D CFD model is applied to 1 kW flowing-gas Cs DPAL [A.V. Bogachev et al., Quantum Electron. 42, 95 (2012)] and the calculated results are in good agreement with the measurements. Comparison of the 2D CFD to semi-analytical model [B. D. Barmashenko and S. Rosenwaks, J. Opt. Soc. Am. B 30, 1118 (2013)] shows that for low pump power both models predict very close values of the laser power; however, at higher pump power, corresponding to saturation of the absorption of the pump transition, the laser power calculated using the 2D CFD model is much higher than that obtained using the semi-analytical model. At high pump power, the heat convection out of the laser resonator is more efficient for the transverse case than the coaxial case, the beam temperature is lower and consequently the calculated laser power is higher. Optimization of the Cs DPAL parameters, using 3D CFD modeling, shows that applying high flow velocity and narrowband pumping, maximum lasing power as high as 40 kW can be obtained at pump power of 80 kW for transverse flow configuration in a pumped volume of ~ 0.7 cm3.