International Journal for Numerical Methods in Fluids

Tezduyar, Tayfun E.; Kawahara, Mutsuto; Hughes, Thomas J. R.

doi: 10.1002/fld.1650211001pmid: N/A

Tezduyar, Tayfun E.; Kawahara, Mutsuto; Hughes, Thomas J. R.

doi: 10.1002/fld.1650211002pmid: N/A

Aliabadi, S. K.; Tezduyar, T. E.

doi: 10.1002/fld.1650211003pmid: N/A

Massively parallel finite element computations of the compressible Euler and Navier‐Stokes equations using parallel supercomputers are presented. The finite element formulations are based on the conservation variables and the streamline‐upwind/Petrov‐Galerkin (SUPG) stabilization method is used to prevent potential numerial oscillations due to dominant advection terms. These computations are based on both implicit and explicit methods and their parallel implementation assumes that the mesh is unstructured. The implicit computations are based on iterative strategies. Large‐scale 3D problems are solved using a matrix‐free iteration technique which reduces the memory requirements significantly. The flow problems we consider typically come from aerospace applications, including those in 3D and those involving moving boundaries interacting with boundary layers and shocks. Problems with fixed boundaries are solved using a semidiscrete formulation and the ones involving moving boundaries are solved using the deformable‐spatial‐domain/stabilized‐space‐time (DSD/SST) formulation.

Farhat, Charbel; Lesoinne, Michel; Maman, Nathan

doi: 10.1002/fld.1650211004pmid: N/A

A three‐field arbitrary Lagrangian‐Eulerian (ALE) finite element/voluem formulation for coupled transient aeroelastic problems is presented. The description includes a rigorous derivation of a geometric conservation law for flow problems with moving boundaries and unstructured deformable meshes. The solution of the coupled governing equations with a mixed explicit (fluid)/implicit (structure) staggered procedure is discussed with particular reference to accuracy, stability, distributed computing, I/O transfers, subcycling and parallel processing. A general and flexible framework for implementing partitioned solution procedures for coupled aeroelastic problems on heterogeneous and/or parallel computational platforms is described. This framework and the explicit/implicit partitioned procedures are demonstrated with the numerical investigation on an iPSC‐860 massively parallel processor of the instability of flat panels with infinite aspect ratio in supersonic airstreams.

Gresho, P. M.; Chan, S. T.; Christon, M. A.; Hindmarsh, A. C.

doi: 10.1002/fld.1650211005pmid: N/A

In an attempt to overcome some of the well‐known ‘problems’ with the Q1P0 element, we have devised two ‘stabilized’ versions of the Q1Q1 element, one based on a semi‐implicit approximate projection method and the other based on a simple forward Euler technique. While neither one conserves mass in the most desirable manner, both generate a velocity field that is usually ‘close enough’ to divergence‐free. After attempting to analyse the two algorithms, each of which includes some ad hoc ‘enhancements’, we present some numerical results to show that they both seem to work well enough. Finally, we point out that any projection method that uses a ‘pressure correction’ approach is inherently limited to time‐accurate simulations and, even if treated fully implicitly, is inappropriate for seeking steady states via large time steps.

Hatanaka, Katsumori; Kawahara, Mutsuto

doi: 10.1002/fld.1650211006pmid: N/A

In this paper the vortex shedding around a heated/cooled circular cylinder is numerically simulated by solving the time‐dependent Navier‐Stokes and energy equations. A finite element method that is referred to as the three‐step Taylor‐Galerkin method is used to compute these equations. The attention of this study is directed to the investigation of the effect of buoyancy on the vortex street behind the cylinder at constant Reynolds number. The present paper shows the suppression or generation of the von Kármán vortex street behind the cylinder when the cylinder surface is heated or cooled respectively. The relationship between the temperature‐induced buoyancy force and the vortex shedding is also discussed through several numerical examples.

Inoue, Yukihiko; Katsuragi, Kazuyuki; Ukai, Osamu; Adachi, Takeshi

doi: 10.1002/fld.1650211007pmid: N/A

This paper describes an efficient parallel algorithm of the cellular automaton (CA) method for microscopic fluid dynamics simulations. The CA method is parallelized with so‐called multispin coding and with one‐dimensional domain decomposition. The parallel CA method has a constant computational load balance and small data transfer between only nearby domains. We have applied the parallel CA method to a large‐scale Poiseuille flow simulation and an immiscible two‐phase flow simulation on a Fujitsu AP1000 with 64 processors.

Johan, Zdeněk; Mathur, Kapil K.; Johnsson, S. Lennart; Hughes, Thomas J. R.

doi: 10.1002/fld.1650211008pmid: N/A

We examine the solution of a practical engineering problem on a parallel computer. The problem involves the steady laminar viscous flow about an ONERA M6 wing and the computer is a 64‐processing‐node Connection Machine CM‐5E. We show that efficient domain decomposition procedures lead to a balanced load on the processors and low communication times. The net result is that solutions can be attained in roughly 20 min elapsed time for a 48,011‐node, 266,566‐element unstructured mesh. We conclude that this is sufficiently fast to support the design process.

Kashiyama, Kazuo; Ito, Hanae; Behr, Marek; Tezduyar, Tayfun

doi: 10.1002/fld.1650211009pmid: N/A

Massively parallel finite element strategies for large‐scale computations of shallow water flows and contaminant transport are presented. The finite element discretizations, carried out on unstructured grids, are based on a three‐step explicit formulation both for the shallow water equations and for the advection‐diffusion equation governing the contaminant transport. Parallel implementations of these unstructured‐grid‐based formulations are carried out on the Army High Performance Computing Research Center Connection Machine CM‐5. It is demonstrated with numerical examples that the strategies presented are applicable to large‐scale computations of various shallow water flow problems.

Liu, Wing Kam; Chen, Yijung

doi: 10.1002/fld.1650211010pmid: N/A

Multiple scale methods based on reproducing kernel and wavelet analysis are developed. These permit the response of a system to be separated into different scales. These scales can be either the wave numbers corresponding to spatial variables or the frequencies corresponding to temporal variables, and each scale response can be examined separately. This complete characterization of the unknown response is performed through the integral window transform, and a space‐scale and time‐frequency localization process is achieved by dilating the flexible multiple scale window function. An error estimation technique based on this decomposition algorithm is developed which is especially useful for local mesh refinement and convergence studies. This flexible space‐scale window function can be constructed to resemble the well‐known unstructured multigrid and hp‐adaptive finite element methods. However, the multiple scale adaptive refinements are performed simply by inserting nodes into the highest wavelet scale solution region and at the same time narrowing the window function. Hence hp‐like adaptive refinements can be performed without a mesh. An energy error ratio parameter is also introduced as a measure of aliasing error, and critical dilation parameters are determined for a class of spline window functions to obtain optimal accuracy. This optimal dilation parameter dictates the number of nodes covered under the support of a given window function. Numerical examples, which include the Helmholtz equation and the 1D and 2D advection‐diffusion equations, are presented to illustrate the high accuracy of the methods using the optimal dilation parameter, the concept of multiresolution analysis and the meshless unstructured adaptive refinements.