International Journal for Numerical Methods in Fluids

Sarrate, J.; Peraire, J.; Patera, A.; Hafez, M.; Heinrich, J.C.

doi: 10.1002/(SICI)1097-0363(19990915)31:1<17::AID-FLD953>3.0.CO;2-Xpmid: N/A

A Neumann subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, constant‐free upper and lower bounds for non‐linear outputs of the Helmholtz equation in two‐dimensional exterior domains is presented. The bound procedure is firstly formulated, with particular emphasis on appropriate extension to complex‐valued equations; then, illustrative numerical examples for outputs, such as the intensity of the scattered wave over a small segment of the domain boundary, are provided. Copyright © 1999 John Wiley & Sons, Ltd.

Carey, G.F.; Mclay, R.; Bicken, G.; Barth, B.; Swift, S.; Ardelea, A.; Hafez, M.; Heinrich, J.C.

doi: 10.1002/(SICI)1097-0363(19990915)31:1<37::AID-FLD954>3.0.CO;2-Spmid: N/A

A domain decomposition strategy and a parallel gradient‐type iterative solution scheme have been developed and implemented for the computation of complex three‐dimensional viscous flow problems involving heat transfer and surface tension effects. Special attention has been paid to the kernels for the computationally intensive matrix–vector products and dot products, to memory management, and to overlapping communication and computation. Details of these implementation issues are described together with associated performance and scalability studies. Representative Rayleigh–Bénard and microgravity Marangoni flow calculations and performance results on the Cray T3D and T3E are presented. Performance studies have been recently carried out and sustained rates above 50 gigaflops and 100 gigaflops have been achieved on the 512‐node T3E‐600 and 1024‐node T3E‐900 configurations respectively. The work is currently being extended to tightly‐coupled parallel ‘Beowulf‐type’ PC clusters and some preliminary performance results on this platform are presented. Copyright © 1999 John Wiley & Sons, Ltd.

Gunzburger, Max D.; Hafez, M.; Heinrich, J.C.

doi: 10.1002/(SICI)1097-0363(19990915)31:1<53::AID-FLD955>3.0.CO;2-Zpmid: N/A

Several issues related to the calculation of flow sensitivities and the solution of flow optimization problems are considered. For the latter, one‐shot Lagrange multiplier methods are presented, as well as sensitivity‐ and adjoint‐based iterative algorithms. A sample application of each method to a specific flow optimization problem is provided. Then some difficulties associated with the practical implementation of the methods are discussed. Particular emphasis is placed on the effect of flow discontinuities on approximate sensitivities and adjoints. A discussion of these issues is given in the context of the Reimann problem for which exact information is known. Copyright © 1999 John Wiley & Sons, Ltd.

Baumann, Carlos Erik; Oden, J. Tinsley; Hafez, M.; Heinrich, J.C.

doi: 10.1002/(SICI)1097-0363(19990915)31:1<79::AID-FLD956>3.0.CO;2-Cpmid: N/A

This paper introduces a new method for the solution of the Euler and Navier–Stokes equations, which is based on the application of a recently developed discontinuous Galerkin technique to obtain a compact, higher‐order accurate and stable solver. The method involves a weak imposition of continuity conditions on the state variables and on inviscid and diffusive fluxes across inter‐element and domain boundaries. Within each element the field variables are approximated using polynomial expansions with local support; therefore, this method is particularly amenable to adaptive refinements and polynomial enrichment. Moreover, the order of spectral approximation on each element can be adaptively controlled according to the regularity of the solution. The particular formulation on which the method is based makes possible a consistent implementation of boundary conditions, and the approximate solutions are locally (elementwise) conservative. The results of numerical experiments for representative benchmarks suggest that the method is robust, capable of delivering high rates of convergence, and well suited to be implemented in parallel computers. Copyright © 1999 John Wiley & Sons, Ltd.

Nakahashi, Kazuhiro; Sharov, Dmitri; Kano, Shintaro; Kodera, Masatoshi; Hafez, M.; Heinrich, J.C.

doi: 10.1002/(SICI)1097-0363(19990915)31:1<97::AID-FLD957>3.0.CO;2-Dpmid: N/A

In this paper, an unstructured hybrid grid method is discussed for its capability to compute three‐dimensional compressible viscous flows of complex geometry. A hybrid of prismatic and tetrahedral grids is used to accurately resolve the wall boundary layers for high‐Reynolds number viscous flows. The Navier–Stokes equations for compressible flows are solved by a finite volume, cell–vertex scheme. The LU‐SGS implicit time integration method is used to reduce the computational time for very fine grids in boundary layer regions. Two kinds of one‐equation turbulence models are evaluated here for their accuracy. The method is applied to computations of transonic flows around the ONERA M5 airplane and ONERA M6 wing, and supersonic shock/boundary layer interacting flows inside a scramjet inlet to validate the accuracy and efficiency of the method. Copyright © 1999 John Wiley & Sons, Ltd.

Löhner, Rainald; Yang, Chi; Baum, Joseph D.; Luo, Hong; Pelessone, Daniele; Charman, Charles M.; Hafez, M.; Heinrich, J.C.

doi: 10.1002/(SICI)1097-0363(19990915)31:1<113::AID-FLD958>3.0.CO;2-Qpmid: N/A

A methodology for the simulation of strongly unsteady flows with hundreds of moving bodies has been developed. An unstructured grid, high‐order, monotonicity preserving, ALE solver with automatic refinement and remeshing capabilities was enhanced by adding equations of state for high explosives, deactivation techniques and optimal data structures to minimize CPU overheads, automatic recovery of CAD data from discrete data, two new remeshing options, and a number of visualization tools for the preprocessing phase of large runs. The combination of these improvements has enabled the simulation of strongly unsteady flows with hundreds of moving bodies. Several examples demonstrate the effectiveness of the proposed methodology. Copyright © 1999 John Wiley & Sons, Ltd.

Agarwal, R.K.; Halt, D.W.; Hafez, M.; Heinrich, J.C.

doi: 10.1002/(SICI)1097-0363(19990915)31:1<121::AID-FLD959>3.0.CO;2-Spmid: N/A

Two compact higher‐order methods are presented for solving the Euler equations in two dimensions. The flow domain is discretized by triangles. The methods use a characteristic‐based approach with a cell‐centered finite volume method. Polynomials of order 0 through 3 are used in each cell to represent the conservation flow variables. Solutions are demonstrated to achieve up to fourth‐order accuracy. Computations are presented for a variety of fluid flow applications. Numerical results demonstrate a substantial gain in efficiency using compact higher‐order elements over the lower‐order elements. Copyright © 1999 John Wiley & Sons, Ltd.

Chattot, Jean‐Jacques; Hafez, M.; Heinrich, J.C.

doi: 10.1002/(SICI)1097-0363(19990915)31:1<149::AID-FLD960>3.0.CO;2-Spmid: N/A

The work presented in this paper shows that the mixed‐type scheme of Murman and Cole, originally developed for a scalar equation, can be extended to systems of conservation laws. A characteristic scheme for the equations of gas dynamics is introduced that has a close connection to a four operator scheme for the Burgers–Hopf equation. The results indicate that the scheme performs well on the classical test cases. The scheme has no tuning parameters and can be interpreted as the projection of an L∞‐stable scheme. At steady state second order accuracy is obtained as a by‐product of the box‐scheme feature. Copyright © 1999 John Wiley & Sons, Ltd.