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Parallelization of 2D Lid-Driven Cavity Flow. Asif Salahuddin Ahmad Sharif Jens Kehne. Objectives. Our objectives. Numerical simulation of fluid dynamics, using the Lattice-Boltzmann method Parallelize the code using MPI Study speedup and scalability

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Parallelization of 2D Lid-Driven Cavity Flow

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## Parallelization of 2D Lid-Driven Cavity Flow

AsifSalahuddin

Jens Kehne

Parallelization of 2D Lid-Driven Cavity Flow

### Objectives

Parallelization of 2D Lid-Driven Cavity Flow

### Our objectives

• Numerical simulation of fluid dynamics, using the Lattice-Boltzmann method

• Parallelize the code using MPI

• Study speedup and scalability

• Allow to run large problem sizes in reasonable time

• Allow to run them at all, for that matter (memory requirements)

Parallelization of 2D Lid-Driven Cavity Flow

### Concept

Parallelization of 2D Lid-Driven Cavity Flow

### The Lattice-Boltzmann method

• The Lattice-Boltzmann equation:

• Velocity directions:

Parallelization of 2D Lid-Driven Cavity Flow

### Top-down vs. bottom-up

Partial

differential

equations

(Navier-Stokes)

Partial

differential

equations

(Navier-Stokes)

Discretization

Multi-scale analysis

Difference

equations

(Conserved Quantities?)

Discrete model (LGCA or LBM)

Parallelization of 2D Lid-Driven Cavity Flow

### Fluid nodes

• The entire problem is represented as a grid of fluid nodes

• Fluid nodes hold velocities towards all neighbors

• New grid state computed for discrete time steps

Parallelization of 2D Lid-Driven Cavity Flow

### Wall bounceback

• The fluid domain is surrounded by walls

• On each timestep, the direction of links hitting a wall is reversed

• Walls may be moving

• Changes the momentum of the fluid close to it

Parallelization of 2D Lid-Driven Cavity Flow

### Implementation

Parallelization of 2D Lid-Driven Cavity Flow

### Domain decomposition

• Each processor processes part of the grid

: Ghost nodes

• Represent border nodesof the neighbors

: Border nodes

• Updated by neighbors

: Inner nodes

• We can update these alone

Parallelization of 2D Lid-Driven Cavity Flow

### Automatic decomposition

• Factorize and merge

• Factorize x and y dimension and #procs

• Divide x and y by prime factors of #procs

• Goal: Try to keep the processor’s grids as square as possible

• Best relation between inner and border nodes

• Minimizes communication

Parallelization of 2D Lid-Driven Cavity Flow

### Automatic decomposition - demo

#CPUs: 6 = 2 * 3

X-axis: 30 = 2 * 3 * 5

Y-axis: 20 = 2 * 2 * 5

30

# CPUs: 6

20

10

10

Parallelization of 2D Lid-Driven Cavity Flow

### Optimizations

• Overlapping wall bounceback and communication

• Overlapping inner node computation with communication

• Massive slowdown!

• Probably due to cache effects

• Making use of regular communication pattern

• Slower (we have no idea why!)

Parallelization of 2D Lid-Driven Cavity Flow

### Experimental results

Parallelization of 2D Lid-Driven Cavity Flow

### Experimental setup

• Lonestar Linux cluster @ University of Texas

• Part of the Teragrid project

• 1300 compute nodes

• 2 Intel Xeon 2.66 GHz dual-core CPUs per node

• 42.6 GFLOPS/node

• 8GB RAM/node

• Linux kernel 2.6, 64 bit

• Infiniband interconnect, fat tree topology

Parallelization of 2D Lid-Driven Cavity Flow

### Actual speedup

Parallelization of 2D Lid-Driven Cavity Flow

### Relation to expected speedup

Parallelization of 2D Lid-Driven Cavity Flow

### Questions

Parallelization of 2D Lid-Driven Cavity Flow