A hybrid adaptive gridding procedure for three-dimensional flow problems

Abstract

A hybrid adaptive gridding procedure which combines both the local refinement method and the global grid moving method is devised. The grid moving method is employed to obtain the initial adaptive solution. The local refinement method is then applied on the large error regions of this initial adaptive solution. The large error regions are flagged by using the weight function approach. The effectiveness of using an adaptive initial solution instead of a uniform grid initial solution is assessed. Use of the weight function as an error indicator is discussed in the computation of the model problems. It is found that an adaptive initial solution reduces the sizes of the large error regions. This can save effort in the later solution refinement. Use of the weight function as an indicator can reduce the effort required for error estimation. The procedure is first verified in the computation of the model equations which have exact solutions. The procedure is then applied to the computation of three-dimensional, steady, laminar flow problems which requires the solutions of the Navier-Stokes equations. The flow problems are a polar cavity flow, a natural convection flow in an enclosure and a curved tube flow. Numerical efficiencies ranging from 30 to 40 are obtained in the model equations. Those for the flow problems are about 20–30. The proposed procedure is most suitable for flows whose high gradient regions are localized in a limited portion of the domain. The most attractive feature of the procedure is its ease of application of practical flow problems.