Showing papers by "Graham F. Carey published in 1995"
TL;DR: In this paper, a higher-order compact scheme that is O(h4) on the nine-point 2D stencil is formulated for the steady stream-function vorticity form of the Navier-Stokes equations.
Abstract: A higher-order compact scheme that is O(h4) on the nine-point 2-D stencil is formulated for the steady stream-function vorticity form of the Navier-Stokes equations. The resulting stencil expressions are presented and hence this new scheme can be easily incorporated into existing industrial software. We also show that special treatment of the wall boundary conditions is required. The method is tested on representative model problems and compares very favourably with other schemes in the literature.
239 citations
TL;DR: In this article, a least-squares finite element formulation of Fisher's equation was developed and supporting numerical studies were carried out, with particular interest associated with the approximation of progressive wave solutions with minimum speed and the viability of the least square approach for this class of problem.
Abstract: Fisher's equation is a classical diffusion–reaction type of problem describing diffusion and nonlinear reproduction of a species. In the present study we develop a least-squares finite element formulation of Fisher's equation and carry out supporting numerical studies. Of particular interest are questions associated with the approximation of progressive wave solutions with minimum speed and the viability of the least-squares approach for this class of problem. © 1995 John Wiley & Sons, Inc.
49 citations
TL;DR: This paper considers an approximate block-factorization technique recently proposed by Chan and Vassilevski and which is well defined for positive definite block-tridiagonal matrices and is analyzed and supported with extensive numerical experiments.
Abstract: The least-squares mixed finite element technique developed in Part I is applied to non-selfadjoint second-order elliptic problems. This approach leads to a symmetric positive definite bilinear form which is coercive uniformly in the discretization parameter. In this paper we consider an approximate block-factorization technique recently proposed by Chan and Vassilevski in [A framework for block-ILU factorization using block size reduction, Math. Comp., 64 (1995), pp. 129–156] and which is well defined for positive definite block-tridiagonal matrices. The method is analyzed and supported with extensive numerical experiments.
33 citations
TL;DR: In this article, a least square finite element analysis of viscous fluid flow together with a trajectory integration technique for tracers is formulated and provided a mechanism for investigating mixing, which was carried out using an improved Heun predictor-corrector.
Abstract: A least‐squares finite element analysis of viscous fluid flow together with a trajectory integration technique for tracers is formulated and provides a mechanism for investigating mixing. Tracer integration is carried out using an improved Heun predictor‐corrector. Results from our supporting numerical studies on the CRAY and Connection Machine (CM) closely resemble the patterns of mixing observed in experiments. A “box‐counting” scheme and other measures to characterize the level of mixing are developed and investigated. This measure is utilized in numerical experiments to determine an optimal forcing frequency for mixing by periodic boundary motion in a rectangular enclosure. Some details concerning the numerical schemes and vector‐parallel implementation are also included.
7 citations
TL;DR: A massively parallel formulation for the solution of the parabolized Navier-Stokes equations has been developed for multiple instruction, multiple data (MIMD) computers, with high parallel efficiency, with fixed solution time as the computational work is scaled with the number of processors.
Abstract: A massively parallel formulation for the solution of the parabolized Navier-Stokes equations has been developed for multiple instruction, multiple data (MIMD) computers. All functionality of the serial version of the code has been preserved in the parallel implementation, including grid generation, linear system solvers, and shock fitting. The computational domain is automatically decomposed and load balanced on individual processing elements. Performance timings are carried out for various MIMD architectures. Numerical tests indicate high parallel efficiency, with fixed solution time as the computational work is scaled with the number of processors. 13 refs.
7 citations
TL;DR: A two-dimensional p-type finite element scheme for distributed parallel computation of viscous flows is developed based on an element-by-element implementation of the Biconjugate Gradient Stabilized 2 iterative method coupled with a recently developed class of block preconditioners.
Abstract: A two-dimensional p-type finite element scheme for distributed parallel computation of viscous flows is developed. The approach is based on an element-by-element implementation of the Biconjugate Gradient Stabilized 2 iterative method coupled with a recently developed class of block preconditioners. Critical to the overall parallel performance is the parallel solution of the imbedded bilinear preconditioner. Performance results are presented for the 2-D driven cavity incompressible viscous flow problem solved using incremental continuation in the Reynolds number on the Intel Touchstone Delta. These results are used to validate a run-time model. The run-time model is then used to examine the scaling properties of the method over a range of p and h.
7 citations
TL;DR: Results indicate that a scheme involving domain decomposition with a Gauss-Seidel type of update for the RK four-stage scheme is most effective and provides performance in excess of 8 Gflops on the Cray C-90.
Abstract: A class of vector-parallel schemes for solution of steady compressible or incompressible viscous flow is developed and performance studies carried out The algorithms employ an artificial transient treatment that permits rapid integration to a steady state In the present work a four-stage explicit Runge-Kutta scheme employing variable local step size is utilized for the ODE system integration The RK-4 scheme is restructured to allow vectorization and enhance concurrency in the calculation for a streamfunction-vorticity formulation of the flow problem The parameters of the resulting RK scheme can be selected to accelerate convergence of the RK recursion Four main procedures are considered which permit vector-parallel solution: a Jacobi update, a hybrid of the Jacobi and Gauss-Seidel method, red-black ordering and domain decomposition Numerical performance studies are conducted with a representative viscous incompressible flow calculation Results indicate that a scheme involving domain decomposition with a Gauss-Seidel type of update for the RK four-stage scheme is most effective and provides performance in excess of 8 Gflops on the Cray C-90
3 citations
TL;DR: In this paper, the authors develop some conformal maps and related strategies for grid generation in certain difficult domains, such as non-convex domains and domains with corners and cusps.
Abstract: We develop some special conformal maps and related strategies for grid generation in certain ‘difficult’ domains. Of particular interest are non-convex domains, and domains with corners and cusps.
2 citations
TL;DR: In this paper, an integrated element-by-element approach to the solution of the governing partial differential equations, and more particularly to the computation of the necessary gradients of the objective function and constraints using an adjoint formulation, is developed.
Abstract: A strategy for the efficient solution of non-linear shape optimization problems is developed. This strategy employs an integrated element-by-element approach to the solution of the governing partial differential equations, and, more particularly, to the computation of the necessary gradients of the objective function and constraints using an adjoint formulation. This proves to be a very efficient strategy and also is relatively easy to implement, because the local effect of design changes can be exploited. The method is tested with an application involving the design of the shape of electromagnet poles in order to obtain a desired field in the interpolar region.
1 citations
TL;DR: In this paper, the effect of upwinding on iterative performance of convection-diffusion problems is investigated and an analysis of the iterative method considered in this paper leads to a criterion for selecting the optimal upwitching parameter to improve the performance of a class of two-dimensional convection diffusion problems.
Abstract: The effect of upwinding on iterative performance of convection–diffusion problems is investigated. An analysis of the iterative method considered here leads to a criterion for selecting the optimal upwinding parameter to improve iterative performance for a class of two-dimensional convection–diffusion problems. Supporting numerical experiments are presented.