Scalability and Performance of Data-Parallel Pressure-Based Multigrid Methods for Viscous Flows

Blosch, Edwin; Shyy, Wei

doi:10.1006/jcph.1996.0098

Cited by 3 publications

(1 citation statement)

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“…However, for large scale problems, other iterative methods with multi-level smoothing are more demanding for the uniform convergence rate. For example, an application of a V-cycle multigrid method was reported in Blosch and Shyy (1996) for steady incompressible Navier -Stokes equations, where satisfactory convergence rate and scalability were achieved.…”

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Large scale numerical simulations for multi-phase fluid dynamics with moving interfaces

Yamashita¹,

Chen²,

Takahashi³

et al. 2008

International Journal of Computational Fluid Dynamics

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This short communication presents our recent studies to implement numerical simulations for multi-phase flows on topranked supercomputer systems with distributed memory architecture. The numerical model is designed so as to make full use of the capacity of the hardware. Satisfactory scalability in terms of both the parallel speed-up rate and the size of the problem has been obtained on two high rank systems with massively parallel processors, the Earth Simulator (Earth simulator research center, Yokohama Kanagawa, Japan) and the TSUBAME (Tokyo Institute of Technology, Tokyo, Japan) supercomputers.Keywords: large-scale computing; direct numerical simulation; multi-phase flow; moving interfaces; volume of fluid Multi-phase flows, such as air/water surface, raindrops, bubbles and sprays, are commonly observed in nature. Including at least two fluids of different physical properties that interact with each other, the multi-phase flows exhibit more complex behaviour compared to the homogeneous fluid.Owing to the progress in both the numerics and the computer hardware, direct numerical simulation (DNS) is getting widely accepted as a useful and increasingly mature tool to investigate the dynamics of multi-phase flows where the interface separating different fluid, like air and water, needs to be explicitly resolved. To this end, a practical code for the DNS of multi-phase fluid dynamics should be able to effectively utilise the parallel computers with distributed memory architectures. Some practices in large scale parallel simulations of multi-phase fluid dynamics with moving interfaces are found in Guler et al. (1999), Xiao (2001, Aliabadi et al. (2002) andSussman (2005).We have recently developed a numerical model for multi-fluid dynamics, based on a so-called one-fluid continuum model (Tryggvason et al. 2006). The numerical model has been built so as to efficiently make use of modern supercomputers with massively parallel architectures of distributed memory. Satisfactory convergence rate and scalability for large scale simulations have been achieved on the Earth simulator (JAMSTEC 2006) and TSUBAME (Endo et al. 2006), two of the top ranked supercomputers in Japan.For incompressible fluid, the governing equations of the one-fluid numerical model for two phase flows involving free interface are written aswhere U ¼ (u x , u y , u z ) is the velocity vector in three dimensions, r is the density and p is the pressure. t ab ¼ m › b u a denotes the components of the viscous shear stress tensor and m the viscosity coefficient. f a is the body force in a-direction and a ¼ x, y, z denotes the direction.Equation (3) is the transport equation of the volume of fluid (VOF) function c which represents the volume fraction of a specified fluid, say the water, in each control volume element. In a one-fluid incompressible model, with the VOF function explicitly computed at each step, the free interface can be uniquely identified, and the physical field of density and other material properties can be straightforwardly specified.As dis...

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