•A technique is presented, for the DNS of turbulent convection in complex domains.•Special near-wall stencils are mapped to the principal mesh for immersed boundaries.•Second-order spatial accuracy is demonstrated to hold also on curved boundaries.•Validation is provided for convection about a tube bundle and turbulent pipe flow. A parallel algorithm is presented for the Direct Numerical Simulation of convection flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary cross-section. The governing equations are discretized by means of the Finite Volume method on Cartesian grids. The method presented includes a triperiodic Poisson solver employed irrespective of the actual boundary shape and a second order accuracy for the computational domain, including the near wall regions, when walls are defined as immersed boundaries. The numerical solution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for laminar and turbulent pipe flow, and for the case of flow around an array of heated cylindrical rods arranged in a triangular lattice. The formal accuracy of the method is demonstrated in laminar flow conditions, and DNS results in turbulent conditions are compared to available literature data, thus confirming the favorable qualities of the method.