Navier-Stokes 2D Open Channel Flow Solver

Introduction

This repository can be seen as an extention of the serial-version of the NavierStokes-2D-ChannelFlow. This version incorporates multithreading via the OpenMP API and is developed in a 'modern' Object Oriented way, rather than the original procedural way. I assume that the user/reader is familar with Fluid Dyanmics and therefore the Navier-Stokes Equations. What I will go over is the Linear Algebraic Solvers: Successive Over-Relaxation (SOR) Method and the Jacobi Iterative Method. I won't be focussing solely on Fortran like I did with the original solver. This time I will look using other languages too. For example:

• Modern C++.
• C.
• Python.
• Rust.

Note

This is a work in progress so it will take time to complete as I will be covering multiple languages. At present, the solver is being developed in Fortran.

The SIMPLE Algorithm

The Navier-Stokes Equations are solved via the SIMPLE algorithm, a widely used numerical procedure in Computational Fluid Dynamics, where the acronym stands for:

• S: Semi-
• I: Implicit
• M: Method (for)
• P: Pressure
• L: Linked
• E: Equations

Mathematics: Numerical Linear Algebra

Successive Over-Relaxation Method

To be completed.

Jacobi Iterative Method

To be completed

Requirements

• Software developed on Ubuntu 20.04.
• Make.
• CMake.
• C++.
• C.
• Fortran.
• Rust.
• Python 3.x.
• Compiler for Modern C++ and C; e.g. g++/gcc 13.1.0 or clang-10.
• Compiler for Fortran: e.g. gfortran.
• Text Editor; any will do.
• OpenMP.
• Knowledge of Fluid Dynamics.
• General knowledge of Applied Mathematics: e.g. Numerical Linear Algebra and Numerical Partial Differential Equations.

Running the Application

• $ git clone https://github.com/MRLintern/Navier-Stokes_2D_Channel-Flow_OpenMP.git