| We describe adaptive grid techniques for elliptic fluid-flow problems. The primary applications are to flows described by the steady, incompressible laminar and Reynolds-averaged Navier-Stokes equations.;Two classes of elliptic flows are identified; they are characterized as having strong or weak viscous-inviscid interactions. Adaptive solution strategies, active and passive, respectively, are developed for each class.;The passive method is applied to linear problems in one and two dimensions. In 2-D, the refined grids automatically align with the flow, thereby minimizing numerical diffusion. The adaptive method is shown to be more efficient than using a uniform fine grid.;The SIMPLER method is used to solve the steady, laminar, incompressible Navier-Stokes equations. Central differencing of the convective terms is implemented with the defect-correction method to stabilize the solution method for all cell Reynolds numbers. Smooth solutions are calculated for cell Reynolds numbers as high as 150, indicating that the commonly used restriction, Re(,(DELTA)x) < 2 is too severe. Uniform grid calculations are performed for the laminar backstep flow. Patankar's power-law scheme is shown to be less accurate than central differencing, and only first-order accurate.;Our method is an extension of a local refinement technique developed by Berger for systems of hyperbolic equations. Local refined grids are overlaid on a coarser base grid. Recursive use of this technique allows an arbitrary degree of grid refinement. In two dimensions, the refined grid consists of uniform rectangles having arbitrary rotation. Regions needing refinement are defined using local error estimates. The base grid remains fixed, and refinements are added as needed.;Richardson-estimated solution and truncation errors are compared to accurate estimates of the same quantities for the backstep flow. The solution error is well predicted. The truncation-error estimates are less accurate, but they reliably indicate where grid refinement is required.;Active-adaptive calculations of the backstep are made, using boundary-aligned refinement. At Re = 100, the adaptive calculation has comparable accuracy, but is six times faster than a uniform-grid calculation; the advantage is greater at higher Reynolds numbers. Adaptive calculations are also made at higher Reynolds numbers. The calculations agree well with the experimental data and other calculations. |
