Typical turbomachinery aerothermal problems of practical interest are characterized by flow structures of wide-ranging scales, which interact with each other. Such multiscale interactions can be observed between the flow structures produced by surface roughness and by the bulk flow patterns. Moreover, additive manufacturing (AM) may sooner or later open a new chapter in the way components are designed by granting designers the ability to control the shape and patterns of surface roughness. As a result, surface finish, which so far has been treated largely as a stochastic trait, can be shifted to a set of design parameters that consist of repetitive, discrete micro-elements on a wall surface (“manufacturable roughness”). Considering this prospective capability, the question would arise regarding how surface microstructures can be incorporated in computational analyses during designing in the future. Semi-empirical methods for predicting aerothermal characteristics and the impact of manufacturable roughness could be used to minimize computational cost. However, the lack of element-to-element resolution may lead to erroneous predictions, as the interactions among the roughness micro-elements have been shown to be significant for adequate performance predictions (Kapsis and He, 2018, “Analysis of Aerothermal Characteristics of Surface Micro-Structures,” ASME J. Fluids Eng., 140(5), p. 051104). In this paper, a new multiscale approach based on the novel block spectral method (BSM) is adopted. This method aims to provide efficient resolution of the detailed local flow variation in space and time of the large-scale microstructures. This resolution is provided without resorting to modeling every single ones in detail, as a conventional large-scale computational fluid dynamics (CFD) simulation would demand, but still demonstrating similar time-accurate and time-averaged flow properties. The main emphasis of this work is to develop a parallelized solver of the method to enable tackling large problems. The work also includes a first of the kind verification and demonstration of the method for wall surfaces with a large number of microstructured elements.