SUMMARYA procedure is given for generating two-dimensional conforming singularity elements from standard conforming elements. Three new elements with qr-..) derivative singularities are introduced. The technique is based on the use of elements defined by numerically integrated shape functions. Special quadrature rules are suggested for triangular elements. The degeneration of these elements to crack tip elements and the direct evaluation near the singularity of element quantities, such as the stress intensity factors, is discussed.
SUMMARYA comparative investigation, based on a series of numerical tests, of two purely explicit and one semi-implicit finite element methods used for incompressible flow computation is presented. The 'segregated' approach is followed and the equations of motion are considered sequentially. The fundamental concepts and characteristics of the formulations and the solution methodology used are described in technical detail. Various modifications to Chorin's projection algorithm are investigated, particularly with respect to their effects on stability and accuracy. The stability of the semi-implicit method is shown to be less restrictive when compared to the explicit methods as the Reynolds number increases. At large time steps the artificial viscosity is also reduced and higher accuracy is obtained. The performance of the methods discussed in this paper is illustrated by the numerical solutions obtained for the cavity flow and flow past a rearward-facing step problems at high Reynolds numbers, and free convection flow problem at high Rayleigh numbers. It is shown that the semi-implicit method needs fewer iterations than the explicit methods, and the accuracy of the present methods is guaranteed by comparison with the existing methods.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.