Understanding the properties of the atmospheric boundary layer (ABL) is essential for wind energy resource assessment. Numerical studies of wind farms in ABL in different environmental, free-atmospheric, and terrain conditions allow one to estimate correct wind forcing, temperature, and moisture properties. With the availability of powerful supercomputers and parallel multi-physics codes, simulations of ABL and wind farms are becoming possible using computationally costly models like large-eddy simulations (LES). In this work, sheared and shear-free cloud-free convective boundary layers (CBL) over a flat and aerodynamically smooth surface are simulated with wall-resolved (WRLES) and wall-modeled LES (WMLES). The zero-pressure-gradient boundary layer is convectively forced by a constant and homogeneous surface buoyancy flux, that grows into a linearly stratified atmosphere with barotropic conditions in the free troposphere above ABL. This configuration represents a typical midday condition over land. As WRLES and direct numerical simulation (DNS) explicitly resolve the near-wall region both spatially and temporally, these techniques are computationally expensive to solve wall-bounded flows. WMLES can address this challenge, as it reduces the computational cost and simulation time by modeling the near-wall region. The mesh discretization, choice of numerical method, wall-modeling, and subgrid-scale (SGS) models required to simulate such ABL flow problems are studied, using the open-source C++ code OpenFOAM. Results of important ABL parameters such as velocity components and their variances, mean buoyancy and its gradient, heat, and buoyancy flux, and temporal evolution of ABL depth are studied and compared against DNS results to validate the WRLES and WMLES. This is a first step towards ABL flow simulation over various environmental, free-atmospheric, and terrain conditions for wind farm applications.