Showing papers by "Graham F. Carey published in 1998"

Free-surface flow over curved surfaces: Part I: Perturbation analysis

Abstract: The standard two-dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is affected by the bed curvature via a decidedly non-hydrostatic pressure distribution. A detailed derivation of a more general equation set is given here in Part I. The method relies upon a perturbation expansion to simplify a bed-fitted co-ordinate configuration of the three-dimensional Euler equations. The resulting equations are essentially the equivalent of the two-dimensional shallow water equations but with curvature included and without the mild slope assumption. A finite element analysis and flume result are given in Part II. © 1998 John Wiley & Sons, Ltd.

Iterative and Parallel Performance of High-Order Compact Systems

Abstract: Representative transport PDE problems in one, two, and three dimensions are approximated by a class of high-order compact (HOC) difference schemes and their iterative and parallel performance are studied. The eigenvalues and condition numbers of the HOC schemes are analyzed and the performance of standard Krylov-space methods is compared for HOC, central differencing, and standard first-order upwinding schemes. Finally, CPU times, MFLOP rates, and speedup curves are presented for fixed-problem-size cases and scaled-problem-size cases.

Free‐surface flow over curved surfaces: Part II: Computational model

Abstract: SUMMARY In Part I a detailed derivation of a more general shallow water equation set was developed via a perturbation analysis. A finite element computational model of these more general equations is now constructed and the model behavior is compared with conventional shallow water formulations applied to an outletworks flume. © 1998 John Wiley & Sons, Ltd. The momentum equations derived in Part I are in non-conservative form and are written for a specific distance above the bed to include effects due to curvature. The standard two-dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is indeed affected by the bed curvature via a decidedly non-hydrostatic pressure distribution. In Part II these equations are depth-integrated and incorporated in a computational model. This form of the equations may be useful in handling non-smooth conditions. The weak form solution for the no-curvature condition that would be encountered downstream of the spillway can be made to properly conserve momentum and mass through a hydraulic jump, whereas other forms of the equations may not. In the case in which there is bed curvature, these equations will contain additional terms due to the bed curvature which, while finite through the jump, will make an additional contribution that can cause an error in the jump location. Therefore, in the vicinity of the jump these equations, which properly conserve mass and momentum for the no-curvature case, will conserve mass precisely in the curved bed state only. Generally, in practical cases the strong jump is restricted to the region downstream of the spillway face where the bed contains no curvature. Several recent finite element schemes for the shallow water equations utilize the Petrov‐ Galerkin approach [1,2] and are considered in Reference [3]. Such a scheme is constructed here for the system developed in Part I to handle bed curvature effects. The treatment proceeds as follows: first the model equations are summarized and an appropriate test function is devised. Next, the finite element Petrov‐Galerkin system is presented and the treatment of boundary * Correspondence to: USAE Waterways Exp. Station, Vicksburg, MS, USA.

Least-squares finite elements for fluid flow and transport

Abstract: SUMMARY The least-squares mixed finite element method is concisely described and supporting error estimates and computational results for linear elliptic (steady diffusion) problems are briefly summarized. The extension to the stationary Navier‐Stokes problems for Newtonian, generalized Newtonian and viscoelastic fluids is then considered. Results of numerical studies are presented for the driven cavity problem and for a stick‐slip problem. # 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids, 27: 97‐107 (1998)

Parallel conjugate gradient performance for least-squares finite elements and transport problems

Abstract: In this study we consider parallel conjugate gradient solution of sparse systems arising from the least-squares mixed finite element method. Of particular interest are transport problems involving convection. The least-squares approach leads to a symmetric positive system and the conjugate gradient scheme is directly applicable. The scheme is applied to both the convection–diffusion equation and to the stationary Navier–Stokes equations. Here we demonstrate parallel solution and performance studies for a representative MIMD parallel computer with hypercube architecture. © 1998 John Wiley & Sons, Ltd.

A least-squares mixed scheme for the simulation of two-phase flow in porous media on unstructured grids

Abstract: A least-squares mixed formulation is developed for simulation of two-phase flow in porous media. Such problems arise in petroleum applications and ground-water flow. An adaptive strategy based on the element residual as an error indicator is developed in conjunction with unstructured remeshing and tested for the two-phase flow of oil and water. An element-by-element conjugate-gradient scheme (EBE-CG) is compared to a band solution algorithm.