Implications of truncating semi-infinite physical domains on the accuracy of the solutions to the N-S equations (Q1100018)

This paper outlines the discrepancies between the numerical solutions obtained from modeling the laminar incompressible flow past a semi- infinite flat plate with a forward-facing step using a mapped plane representing the entire semi-infinite domain of interest and those obtained from a truncated physical domain. Special emphasis is given to the implications of describing far-field physical boundary conditions on the boundaries of the truncated physical domain and their consequence on the accuracy of the numerical results. In this comparative study, two different formulations of the governing equations are used. Namely, the vorticity-stream function formulation and the primitive variable formulation with pseudo-compressibility. Here, we utilize the former formulation to describe the flow in the truncated physical domain and the latter to describe the flow in a computational plane which represents the image of the semi-infinite physical plane. The discretized forms of the transport equations are then numerically solved using a flux-corrected, explicit finite-difference scheme. Numerical results are given and comparison studies are made for the model problem. The results are also compared with the available experimental data to determine their relative accuracy. The numerical results indicate the inaccuracy of the solutions obtained from the truncated physical domain as compared to those obtained from the computation involving the semi-infinite domain.