Massively parallel finite element simulation Of compressible and incompressible flows

We present a review of where our research group stands in parallel finite element simulation of flow problems on the Connection Machines, an effort that started for our group in the fourth quarter of 1991. This review includes an overview of our work on computation of flow problems involving moving boundaries and interfaces, such as free surfaces, two-liquid interfaces, and fluid-structure and fluid-particle interactions. With numerous examples, we demonstrate that, with these new computational capabilities, today we are at a point where we routinely solve practical flow problems, including those in 3D and those involving moving boundaries and interfaces. We solve these problems with unstructured grids and implicit methods, with some of the problem sizes exceeding 5 000 000 equations, and with computational speeds up to two orders of magnitude higher than what was previously available to us on the traditional vector supercomputers.

[1]  Peter Hansbo,et al.  A velocity pressure streamline diffusion finite element method for Navier-Stokes equations , 1990 .

[2]  S. Mittal,et al.  Space-time finite element computation of incompressible flows with emphasis on flows involving oscillating cylinders , 1991 .

[3]  S. Mittal,et al.  A finite element study of incompressible flows past oscillating cylinders and aerofoils , 1992 .

[4]  D. Coles.  Transition in circular Couette flow , 1965, Journal of Fluid Mechanics.

[5]  C. Kato,et al.  Large eddy simulation of unsteady turbulent wake of a circular cylinder using the finite element method , 1991 .

[6]  Tayfun E. Tezduyar,et al.  SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations , 1993 .

[7]  Marek Behr,et al.  Parallel finite-element computation of 3D flows , 1993, Computer.

[8]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[9]  T. Tezduyar,et al.  Space-time finite element computation of compressible flows involving moving boundaries and interfaces☆ , 1993 .

[10]  S. Mittal,et al.  Massively parallel finite element computation of incompressible flows involving fluid-body interactions , 1994 .

[11]  Daniel R. Lynch,et al.  Unified approach to simulation on deforming elements with application to phase change problems , 1982 .

[12]  J. G. Kennedy,et al.  Computation of incompressible flows with implicit finite element implementations on the Connection Machine , 1993 .

[13]  Z. C. Feng,et al.  Symmetry-breaking bifurcations in resonant surface waves , 1989, Journal of Fluid Mechanics.

[14]  M. Païdoussis,et al.  Dynamic stability of pipes conveying fluid , 1974 .

[15]  T. Tezduyar,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests , 1992 .

[16]  Tayfun E. Tezduyar,et al.  Finite element computation of compressible flows with the SUPG formulation , 1991 .

[17]  Thomas J. R. Hughes,et al.  Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations , 1983 .

[18]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems , 1987 .

[19]  S. Mittal,et al.  Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements , 1992 .

[20]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[21]  Tayfun E. Tezduyar,et al.  Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces , 1994 .

[22]  Tayfun E. Tezduyar,et al.  PARALLEL FINITE ELEMENT SIMULATION OF 3D INCOMPRESSIBLE FLOWS: FLUID-STRUCTURE INTERACTIONS , 1995 .

[23]  Marek Behr,et al.  Finite element solution strategies for large-scale flow simulations☆ , 1994 .

[24]  Marek Behr,et al.  Implementation of implicit finite element methods for incompressible flows on the CM-5 , 1994 .

[25]  F. Shakib.  Finite element analysis of the compressible Euler and Navier-Stokes equations , 1989 .

[26]  H. Schlichting.  Boundary Layer Theory , 1955 .

[27]  S. Mittal,et al.  Computation of unsteady incompressible flows with the stabilized finite element methods: Space-time formulations, iterative strategies and massively parallel implementations , 1992 .

[28]  Peter Hansbo,et al.  A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equation , 1990 .

[29]  S. Mittal,et al.  Massively parallel finite element computation of three dimensional flow problems , 1992 .

[30]  T. Hughes,et al.  Space-time finite element methods for elastodynamics: formulations and error estimates , 1988 .

[31]  M. Behr,et al.  Finite element solution strategies flow simulations , 1994 .

[32]  Tayfun E. Tezduyar,et al.  SUPG finite element computation of compressible flows with the entropy and conservation variables formulations , 1993 .

[33]  J. Reddy,et al.  Advances in finite element analysis in fluid dynamics - 1991; Proceedings of the Symposium, ASME Winter Annual Meeting, Atlanta, GA, Dec. 1-6, 1991 , 1991 .

[34]  Tayfun E. Tezduyar,et al.  Parallel fluid dynamics computations in aerospace applications , 1995 .

[35]  S. Mittal,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. II: Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders , 1992 .

[36]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .