It is well known that for small Reynolds numbers, flow around a cylinder is laminar and stable. For larger Reynolds numbers, although the flow regime remains laminar, the formation of complex periodic structures appear downstream. The cyclic nature of this periodic flow is well characterized by the vortex shedding frequency and Strouhal number. However, complexities of these periodic structures downstream continue to be a topic of research. Periodic laminar 2D incompressible viscous flow around a cylinder is simulated using OpenFoam, an open source computational fluid dynamics program. To better understand these complex structures downstream, a customized computer graphical tool, VerFlow-V.01, was created to analyze and study OpenFoam simulation results. This study includes an investigation of calculating the details of drag and lift coefficients for the cylinder using mathematical models that integrate properties in subdomains, an approach not previously explored to the knowledge of the author. Numerical integration is accomplished using a finite difference approach for solving surface and contour integrals in subdomains of interest. Special attention is given to pressure and to the second invariant of the velocity gradient, as they have a clear mathematical relationship, which is consistent with results previously published. A customized visual data analysis tool, called VerFlow-V.01, allowed investigators to compare simulation data variables in a variety of useful ways, revealing details not previously understood. Main subroutines and a user's manual are included as appendices to encourage reproducibility and future development of the numerical, analytical and graphical models developed here. Together these models resulted in a new understanding of periodic laminar flow around a cylinder. A unique approach was developed to qualitatively understand the origins of drag and lift coefficients associated with properties mapped as images in subdomains of interest downstream. These results explain the development of convergent, eddy, and stream zones embedded in flow fields downstream.