Use of improved far-field boundary conditions to compute external flows on reduced domains.

摘要

Viscous incompressible flow past a finite axisymmetric body in an unbounded domain is considered computationally. The domain is divided into viscous interior and inviscid exterior regions by a paraboloidal artificial boundary, and is truncated at some distance downstream. We develop conditions on this artificial boundary that allow an analytical solution of the potential flow equations, the known asymptotic form of the Navier-Stokes equations, in the inviscid region to be matched to a numerical solution of the full Navier-Stokes equations in the viscous region. The domain convergence and efficiency of the approach are compared to currently-used far-field boundary conditions for flows past a sphere and a finite paraboloidal body of revolution. We show that our conditions give exponential convergence with respect to upstream domain length, which is much faster than that for common alternatives, allowing a substantially reduced computational domain.; Our computational results for flow past a sphere are in excellent agreement with previous computations and empirical correlations of experimental and computational results.; We have also used this computational approach to study, for the first time, flow past a convex axisymmetric body formed by a finite paraboloid with a paraboloidal surface closing the aperture. Converged flows were computed for three different aspect ratios up to a Reynolds number (Re) of 200. For sufficiently small Re, there is no separation. For an intermediate range of Re, the separation point moves from the rear stagnation point towards the edge of the body as Re increases. Beyond some Re, the computed separation circle lies between the edge and nearest grid point, for all grid spacings considered. The length of the separated flow region varies approximately with a fractional power of the logarithm of the Reynolds number. The computational advantages of the present approach are demonstrated by comparing memory usage and runtime for solutions of comparable accuracy. When the system of nonlinear algebraic equations is solved by Newton iteration, memory usage and runtime are reduced by about 70% compared to computations using Neumann and free-stream Dirichlet boundary conditions.