## CFD101: 2D Lid Driven Cavity Flow

Version 1.2.1 (56.2 MB) by
This repository provides MATLAB code for the lid-driven cavity flow where incompressible Navier Stokes equation is numerically solved using

Updated 22 Mar 2023

From GitHub

# 2D Lid Driven Cavity Flow

This repo provides a MATLAB example code for the lid-driven cavity flow where incompressible Navier Stokes equation is numerically solved using a simple 2nd order finite difference scheme on a staggered grid system.

(Left: Re = 100, Right: Re = 10,000)

The arrow denotes the velocity field, and the contour denotes its magnitude.

## Part 1: Getting Started with the Cavity Flow

• 日本語のドキュメントはこちら から

The numerical scheme is kept primitive; the explicit treatment of viscous term (the solution diverges at low Reynolds number), and the time integration is Euler.

まずは単純な手法でキャビティ流れのシミュレーションを実施します。

## Part 2: Implicit Scheme for the Viscous Terms

• 日本語のドキュメントはこちら から

The implicit treatments for viscous terms are implemented, namely the Crank-Nicolson method. For better stability for non-linear terms, Adams-Bashforth, and 3 steps-Runge-Kutta is also implemented.

## Part 3: Performance Comparison of the Implicit Methods

• 日本語のドキュメントはこちら から

The implicit treatments for viscous terms results in solving the discretized Helmholtz equation at every time step. We compare the performance of five methods.

## Part 4: Validation of the Numerical Scheme

• Click [here] for detailed documentation in English. (not ready)
• 日本語のドキュメントはこちら から

The results of spatial and temporal convergence tests are shown. Convergence tests are run using the method of manufactured solutions where the Navier-Stokes equations are forced so that the solution will be a prescribed time-dependent function.

ある外力項を加えた Navier-Stokes 方程式の数値解と解析解と比較することで、時間積分の精度（1次精度） と空間微分の精度（2次精度）を確認します。

## Next to come

The plan is to allow arbitrary boundary conditions for more fun simulations.

# Environment

• MATLAB R2019b
• Signal Processing Toolbox if you use dct in solving Poisson eqn.

# ToDo

1. Implement implicit treatment of viscous terms
2. Implement crank-Nicolson for the non-linear terms
3. Allow obstacles within the domain
4. Allow inflow from the wall
5. Make it to 3D

--

Copyright (c) 2020, The MathWorks, Inc.

### Cite As

michio (2023). CFD101: 2D Lid Driven Cavity Flow (https://github.com/mathworks/2D-Lid-Driven-Cavity-Flow-Incompressible-Navier-Stokes-Solver), GitHub. Retrieved .

##### MATLAB Release Compatibility
Created with R2019b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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#### docs_part4

Version Published Release Notes
1.2.1

change the Description to use README.md from GitHub

1.2.0

Added part 3: Performance Comparison of the Implicit Methods

1.1.1

Updated Description

1.1.0

Added part 2 documentation. Crank-Nicolson and Adams-Bashforth, 3 steps Runge-Kutta are implemented.

1.0.4

Update solvePoissonEquation_direct.m, eliminate re-creating A matrix by the use of persistent variable

1.0.3

Update GitHub URL

1.0.2

Update the thumbnail GIF

1.0.1

Changed the title

1.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.