TY - JOUR

T1 - Grouped element-by-element iteration schemes for incompressible flow computations

AU - Tezduyar, T. E.

AU - Liou, J.

N1 - Funding Information:
Management of the linear equation systems encountered in the finite element formulation of incompressible flows becomes an important task when we attempt to solve large-scale problems. The large global matrices involved in such linear equation systems arise usually from implicit time-integration of spatially discretized time-dependent equations or simply from spatial discretization of time-independent equations. For example, the incompressible Navier— Stokes equations in the vorticity-stream function formulation involve a time-dependent convection—diffusion equation for the vorticity and a Poisson’s equation for the stream function. In direct (nomterative) treatment of these linear equation systems, the storage need for the global matrices involved and the CPU time requirement for the actual solution process can become too heavy to handle even for the largest and fastest supercomputers available today. Espe- The EBE impleme~ttations in computational * This research was sponsored by NASA-Johnson fluid dynamics were first reported, in the context Center under contract NAS-9-17892 and by NSF of compressible Euler equations, by Hughes, grant MSM-8796352. Winget, Levit and Tez~iuyar\[1\]E. arlier implemen-OO1O-4655/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) In this paper we describe, in the context of the vorticity-stream functipn formulation, alternative solution techniques w~iicheliminate the need for the storage and factorization of large global matrices.

PY - 1989/5

Y1 - 1989/5

N2 - Grouped element-by-element (GEBE) iteration schemes for incompressible flows are presented in the context of vorticity- stream function formulation. The GEBE procedure is a variation of the EBE procedure and is based on arrangement of the elements into groups with no inter-element coupling within each group. With the GEBE approach, vectorization and parallel implementation of the EBE method becomes more clear. The savings in storage and CPU time are demonstrated with two unsteady flow problems.

AB - Grouped element-by-element (GEBE) iteration schemes for incompressible flows are presented in the context of vorticity- stream function formulation. The GEBE procedure is a variation of the EBE procedure and is based on arrangement of the elements into groups with no inter-element coupling within each group. With the GEBE approach, vectorization and parallel implementation of the EBE method becomes more clear. The savings in storage and CPU time are demonstrated with two unsteady flow problems.

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U2 - 10.1016/0010-4655(89)90177-X

DO - 10.1016/0010-4655(89)90177-X

M3 - Article

AN - SCOPUS:0024665549

SN - 0010-4655

VL - 53

SP - 441

EP - 453

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 1-3

ER -