Tianliang Yang

Parallelization of a Modern CFD Incompressible Turbulent Flow Code

Publisher Summary This chapter outlines the numerical analysis and turbulence modeling of a new large-eddy simulation technique for incompressible flows. It is shown that many opportunities for parallelization occur for the chosen algorithmic structure, and reasonably good speedups with increasing number of processors is observed through 32 processors for a message passing interface (MPI) implementation on a HP SuperDome, even with only partial parallelization. In particular most (but not all) commercial CFD software is based on one form or another of the SIMPLE algorithm. These basic approaches are not efficient for time-dependent simulations that are becoming increasingly more widely performed as computing power continues to improve. The parallelization of these commercial codes in almost all cases has been done long after the codes were originally constructed—that is, they were not designed to be parallelized at the time they were initially coded.

Local Discrete-Operator Interpolation Solution of the Phase-Field Model

This paper reports continuing work on application of discrete-operator interpolation (DOI) in solving the one-dimensional phase-field model applied to melt-front tracking. DOI is a numerical technique for computing function values not computed at the original grid points of a finite-difference (or finite element) scheme so as to satisfy the discrete governing equations at the new points. The previous study showed that the DOI technique works quite well for the phase-field model problem. The shortcoming of earlier work was global (in space) application of DOI. Due to the fact that at any instant in time, the melt-front of the phase-field model exists within only a small region of space, it is more efficient to employ a local DOI technique. Local DOI interpolates the numerical solutions only in the melt-front region while a standard numerical method is applied in other regions. In this paper, we describe the phase-field model together with the details of the local DOI method and their numerical implementations. The results of the phase-field model are obtained using a Crank-Nicolson finite-difference scheme. The local DOI results are compared with direct numerical simulation results obtained on a very fine grid to demonstrate the advantages of this method.Copyright

Parallelization of Phase-field Model for Phase Transformation Problem

Publisher Summary This chapter focuses on parallelization of a 2D phase-field model for freezing into supercooled melt of a pure substance using OpenMP. The computational results presented here provide dendrite structures during their formation and evolution. The speedup factor displays a monotone increase with number of processors through 32. However, since the speedup increases only sub-linearly as the number of processors increase, it is clear that the parallel efficiency becomes quite low if more than 16 processors are employed. It introduces the equations of the phase-field model along with the scalings employed to render them dimensionless. Boundary and initial conditions required to formulate a well-posed mathematical problem are also prescribed. Parallelization of the numerical solution procedure is based on the shared-memory programming paradigm using the HP FORTRAN 90 HP-UX compiler. The program is parallelized using OpenMP running on the HP SuperDome at the University of Kentucky Computing Center. The chapter also introduces the phase-field model and briefly discusses numerical procedures and specific problem parameters. It then discusses the approach employed for parallelization, present computed results, and the speedups obtained.

Parallelization of a Genetic Algorithm for Curve Fitting Chaotic Dynamical Systems

This paper is focused on parallelization of a genetic algorithm for a chaotic dynamical system analysis procedure employed in a curve-fitting method for modeling chaotic time series using MPI programming. Relatively good parallel performance is obtained. An experimental turbulent velocity time series is modeled using the parallelized genetic algorithm, and the modeled time series compares favorably with the laboratory measurements.