Details

Autor(en) / Beteiligte

• CHOI, DOCHUL

Titel

COMPUTATION OF INCOMPRESSIBLE FLOW BY A COUPLED IMPLICIT SCHEME (FLUID MECHANICS, COMPUTATIONAL DYNAMICS, NUMERICAL METHOD)

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

1985

Link zum Volltext

• ProQuest

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• The Linearized Block Alternating-direction Implicit (LBI) scheme is studied to obtain steady state solutions of incompressible flow equations in generalized coordinates. The LBI scheme is applied to the incompressible equations by adding an artificial time derivative to the continuity equation. This modification allows both the pressure and velocity to be obtained implicitly, in a fully coupled manner. Two-dimensional inviscid solutions are attempted in two ways: by applying the LBI scheme to the hyperbolized incompressible equations, and by applying the scheme to preconditioned compressible equations. The preconditioning procedure is developed to achieve rapid convergence at the incompressible limit (low Mach number) of compressible flow equations. This procedure makes the convergence rate independent of Mach number and restores the convergence rates which are characteristic of high subsonic Mach numbers. Converged flowfields from both sets of equations are identical and agree well with those obtained from the Douglas-Neumann program. Stability characteristics of the scheme are carefully studied through Fourier analyses in vector form. These analyses can be used to check instability and to predict and control the rate of convergence of the scheme. For two-dimensional cases, the LBI scheme is stable at all Reynolds numbers, and it allows the convective term to be central differenced without any numerical dissipation, even in the inviscid limit. For three-dimensional cases, the LBI scheme has a rather restrictive stability limit. This limit can be alleviated by using explicit and implicit numerical dissipation. The stability limit and the optimum combination of explicit and implicit numerical dissipation are computed. Boundary conditions based on the method of characteristics are developed and applied implicity for the inviscid case and the inviscid region of the viscous case. The proper application of boundary conditions and, in particular, the use of implicit boundary procedures are critical to achieving the most rapid convergence over the widest range of conditions. Applications to Navier-Stokes equations are done for a series of two-dimensional unstaggered cascade problems, and demonstrate the validity of the Fourier stability analyses. The converged results are checked with the solutions based on the boundary-layer equations.