Development of Finite Element Analysis System for Unsteady, Incompressible Viscous Fluid Flows

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The aim of the present research is to develop a numerical procedure for solving the time-dependent, incompressible Navier-Stokes equations, and to implement the procedure as a program system which is applicable to various unsteady flow problems.The followings are the summary of the promotion and the results of the present project.(1) Development of finite element solution procedure: A set of non-linear recurrence equations, which represent evolution of the velocities and the pressures under the incompressibility constraint, are derived from the finite element equations of the primitive variable formulation, by using a unique direct time integration method developed by the investigators and particular processes regarding the continuity conditions and the boundary conditions. Excessively artificial techniques have not been introduced into the present derivation. An iteration process with respect to the non-linear convection terms is performed in every integration step.(2) Implementation … More of finite element program system: Since the system coefficient matrix of the derived non-linear recurrence equations is non-symmetric and may possess a band-profile, the LDU decomposition method using skyline storage is adopted as the equation solver. As far as the time integration interval is fixed, only one factorization need be performed and, after that, only the forward reduction/back substitution of the factorized array need be repeated. Several types of post-processors are prepared in order to express graphically the spatial distribution or the time history of velocity, pressure, streamlines, vorticity, fluid forces, or so on.(3) Verification of the performance of the present analysis system: Comparisons of the numerical results, including vortex shedding problems which require solving large system matrix equations, with experimental observation and measurements show that, the time-dependent solutions agree fairly well with the experimentally visualized flow field, and the fluid forces acting on the obstacles can be predicted. Less