Showing papers by "Graham F. Carey published in 1986"

Element-by-element linear and nonlinear solution schemes

Abstract: The preconditionded conjugate gradient method for solving a linear algebraic system of equations is recast to a form that permits sequential element-by-element calculations suitable for computations with finite element methods. This strategy has been implemented for solving the linear systems arising in a finite element approximation for the standard test example of Laplace's equation. The element-by-element strategy has also been applied to the sequence of linear systems obtained using a successive approximation scheme for a representative class of nonlinear problems. Little storage is needed for these schemes, and test computations have been made on microprocessor, minicomputer, main-frame computers and special processors. The approach also appears appealing for calculations on parallel processors since individual element computations can be done in parallel.

Parallelism in finite element modelling

Abstract: Parallel processes can be identified at several different levels in the computational simulation of physical processes and problems. We first briefly sketch the main steps involved in modelling physical processes and give examples where inherent parallelism is evident. We then proceed more specifically to describe both inherent and induced parallelism that occur when finite element methods are applied to the solution of boundary and evolution problems, and indicate several opportunitites for parallel processing in finite element analysis.

Shock‐free redesign using finite elements

Abstract: A finite element formulation and algorithm for calculation of shock-free compressible flows and design of shockless airfoils is developed The formulation is conceptually similar to current finite difference methods in that it combines the use of a fictitious gas for a regularized compressible potential flow calculation, together with the method of characteristics in the supersonic pocket The redesigned shock-free airfoil surface is determined from a subsidiary streamline calculation In the present analysis, a variational finite element method is used and optimal control techniques are employed to compute the solution to the discrete problem Numerical results and comparison studies with finite difference results for a representative case are given

Stability of penalty finite-element methods for nonconforming problems

Abstract: Penalty methods have been proposed as a viable method for enforcing interelement continuity constraints on nonconforming elements. Particularly for fourth-order problems in which C1-continuity leads to elements of high degree or complex composite elements, the use of penalty methods to enforce the C1-continuity constraint appears promising. In this study we demonstrate equivalence of the finite-element penalty method to a hybrid method and provide a stability analysis which implies that the penalty method is stable only if reduced integration of a certain order is used. Numerical experiments confirm that the penalty method fails if this condition is not met.

Turbulent boundary‐layer analysis using finite elements

Abstract: The use of finite element methods for turbulent boundary-layer flow is relatively recent and of limited extent.1 In the present study, we extend the group variable approach of Fletcher and Fleer2,3 to treat turbulent boundary layer flows with heat transfer using a two-equation turbulence model. The main concepts in the formulations include a Dorodnitsyn-type transformation which uses a velocity component as the transverse variable, a ‘variational’ formulation for the transformed equations using special test functions and development of a two-equation turbulence model in terms of the turbulent kinetic energy and turbulence dissipation rate as additional field variables. Several numerical test cases have been examined comparing the results with finite difference calculations and comparing the two-equation turbulence model with an algebraic turbulence model.

Local pressure oscillation and boundary treatment for the 8-node quadrilateral

Abstract: The 8-node (serendipity) velocity basis with C° bilinear pressure is a popular element but has been observed to yield poor pressures. We present some details of numerical experiments that indicate the local nature of the error and the effects of mesh refinement, increasing Reynolds number and regularity of the data. This leads to a strategy for appropriately modifying the data near the corners that is effective in improving the computed pressure approximation.