Showing papers by "Graham F. Carey published in 1984"
TL;DR: In this paper, a penalty formulation of the stationary Navier-Stokes equations for an incompressible fluid is presented, subject to restrictions on the viscosity and prescribed body force, and it is shown that there exists a unique solution to this penalty problem.
60 citations
Journal Article•
38 citations
01 Jan 1984
TL;DR: In this paper, the authors consider finite difference and finite element approximations to the solution of the multiphase, multicomponent problems and consider the problem of efficient integration, by means of system integrators, of the resulting semidiscrete finite difference or finite element systems for a certain class of flows.
Abstract: The authors consider finite difference and finite element approximations to the solution of the multiphase, multicomponent problems. They also consider the problem of efficient integration, by means of system integrators, of the resulting semidiscrete finite difference or finite element systems for a certain class of flows. Techniques which incorporate adaptive timestep control are utilized. In this way they are able to adaptively control the integration process for problems in which the system stiffness may vary markedly. Representative examples in one and two dimensions corresponding to an enhanced oil recovery process (micellar-polymer flooding) are computed. Numerical results obtained using finite difference and finite element methods are presented in the one-dimensional case. Some new ideas related to adaptive upwinding in the finite element computations are used to control oscillatory overshoot. Both streamline finite difference and general two-dimensional finite difference schemes are described and applied in flow simulations.
19 citations
Journal Article•
TL;DR: In this paper, the authors consider finite difference and finite element approximations to the solution of the multiphase, multicomponent problems and consider the problem of efficient integration, by means of system integrators, of the resulting semidiscrete finite difference or finite element systems for a certain class of flows.
Abstract: The authors consider finite difference and finite element approximations to the solution of the multiphase, multicomponent problems. They also consider the problem of efficient integration, by means of system integrators, of the resulting semidiscrete finite difference or finite element systems for a certain class of flows. Techniques which incorporate adaptive timestep control are utilized. In this way they are able to adaptively control the integration process for problems in which the system stiffness may vary markedly. Representative examples in one and two dimensions corresponding to an enhanced oil recovery process (micellar-polymer flooding) are computed. Numerical results obtained using finite difference and finite element methods are presented in the one-dimensional case. Some new ideas related to adaptive upwinding in the finite element computations are used to control oscillatory overshoot. Both streamline finite difference and general two-dimensional finite difference schemes are described and applied in flow simulations.
9 citations
TL;DR: A finite element method for solution of the stream function formulation of Stokes flow is developed and successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule.
Abstract: SUMMARY A finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non-conforming (C") triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter-element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.
5 citations