Lid-Driven Cavity Project

This project implements a parallel numerical code to solve the vorticity-streamfunction formulation of the incompressible Naiver-Stokes equation in 2D using the finite difference method. In other words, it presents a solver for the lid-driven cavity problem. Output of solver is used to generate data points that map velocity, vorticity and streamfunction values at different grid locations. Full report can be found here.

Pre-requisites

Please make sure the libraries below are installed on the system before running the code:

• BLAS - linear algebra package to perform basic vector and matrix multiplication
• BLACS - linear algebra oriented message passing interface (MPI)
• Boost - utilise the program_options library to obtain program options from command line
• LAPACK - linear algebra package to solve systems of simultaneous linear equations in serial
• MPI - message passing interface for parallel programming
• ScaLAPACK - linear algebra package to solve systems of simultaneous linear equations in parallel

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UNIX/Linux

Compile the program

Navigate to the directory containing all source codes, then enter the following commands accordingly:

make

The Makefile will compile the program and produce the executable Solve file.

Run test cases

One serial and one parallel test cases are declared in the Makefile for validation purposes. Their parameters are:

• Lx = Ly = 1.0
• Nx = Ny = 5
• dt = 0.0001
• T = 1.0
• Re = 100

Serial test case

Run with single process (--np 1) and Px = Py = 1:

make testSerial

Parallel test case

Run with 4 processes (--np 4) with Px = Py = 2, Px * Py = 4:

make testParallel

Output of the tests will be in the Plot/ folder.

Run Cases

Shell script named RunSolver.sh batch runs the solver with given parameters:

./RunSolver.sh

• Lx = 1.0, Ly = 1.0, Nx = 161, Ny = 161, dt = 0.0005, T = 1.0, Re = 100
• Lx = 1.0, Ly = 1.0, Nx = 161, Ny = 161, dt = 0.0005, T = 1.0, Re = 400
• Lx = 1.0, Ly = 1.0, Nx = 161, Ny = 161, dt = 0.0005, T = 5.0, Re = 1000
• Lx = 1.0, Ly = 1.0, Nx = 161, Ny = 161, dt = 0.0005, T = 10.0, Re = 3200
• Lx = 1.0, Ly = 2.0, Nx = 161, Ny = 161, dt = 0.0005, T = 1.0, Re = 100
• Lx = 2.0, Ly = 1.0, Nx = 161, Ny = 161, dt = 0.0005, T = 1.0, Re = 100

16 processes (--np 16), Px = Py = 4 are used for the runs. Output is saved in the Plot/ folder in a <Lx>_<Ly>_<Nx>_<Ny>_<Re>_data.txt format.

Clean folder

To remove generated files, run the following commands:

Remove generated object files (*.o)

make clean

Remove generated data file (*.txt)

make cleanPlot

Remove all generated files

make cleanAll

Usage

Once the solver has been compiled, it can be used via the format

mpiexec --np <no. of procs> ./Solve [options] [args]

options:
--help         prints help message
--Lx <double>  length of domain in the x-direction
--Ly <double>  length of domain in the y-direction
--Nx <int>     number of grid points in the x-direction
--Ny <int>     number of grid points in the y-direction
--Px <int>     number of partitions in the x-direction
--Py <int>     number of partitions in the y-direction
--dt <double>  time step size
--T <double>   final time
--Re <double>  Reynolds number

Directory Files

• assignment.pdf - HPC coursework assignment brief
• Lid-Driven-Cavity.ipynb - A seperate Python implementation of a serial lid-driven cavity solver
• LidDrivenCavity.cpp - Implement serial and parallel LidDrivenCavity class member functions
• LidDrivenCavity.h - Header file for the LidDrivenCavity class
• LidDrivenCavitySolver.cpp - Accept options for the solver and sets up the solver for the lid-driven cavity problem
• Makefile - Compilation of executable, cleaning, and test cases
• ./Plot/ - Folder containing output data of the solver to generate plots
• PoissonSolver.cpp - Implement serial and parallel PoissonSolver class member functions
• PoissonSolver.h - Header file for the PoissonSolver class
• README.md - README markdown file
• repository.log - Git repository log file
• RunSolver.sh - Shell script to run solver and produce required data
• SpeedBatch.sh - Shell script to batch run solver for different number of processes and output time taken

Output files from running different scripts:

• executionTimes.txt - Text file containing run times for different number of processes. Output of ./SpeedBatch.sh
• LidDrivenCavity.o - Object file of LidDrivenCavity.cpp from running make
• LidDrivenCavitySolver.o - Object file of LidDrivenCavitySolver.cpp from running make
• PoissonSolver.o - Object file of PoissonSolver.cpp from running make
• ./Plot/*.txt - Text files containing data produced from running ./Solve
• ./Solve - Executable linking LidDrivenCavitySolver.o, LidDrivenCavity.o and PoissonSolver.o