Modal analysis for incompressible fluid flow: Proposed treatment of inlet and outlet boundary conditions

This paper presents a numerical method for incompressible fluid flow. One challenge in analyzing incompressible fluid flow is that the continuity equation for such flow has no time evolution term. In the pressure correction approach, Poisson's equation is solved iteratively, which takes most of the computational time. In our previous study, modal analysis was proposed for analyzing two-dimensional incompressible fluid flow, which avoids pressure variables and thus iterative calculation of Poisson's equation. In this paper, we propose treating the inlet and outlet boundary conditions. Numerical results for a simple flow system and a step flow obtained using the proposed method are compared with those obtained using the artificial compressible method and the simplified marker and cell (SMAC) method. The results agree well, thereby validating the proposed boundary treatment, and the present modal analysis with a graphics processing unit is 20 times faster than the SMAC method.