Understanding FVM(Lax Friedrich scheme) by solving Burger equation

Finite Volume Method is one of the popular numerical methods used by engineers, mathematicians around the world for solving complex differential equations. This is because it has the characteristics to produce accurate and stable solutions. So, studying the finite volume method is important for an engineer. In this project, you will learn how the Finite Volume Method (Numerical Method) is implemented to solve the differential equation by solving a fluid flow problem using Burger equation.

Read more..

Understanding FVM(Lax Friedrich scheme) by solving Burger equation project Looking to build projects on Mechanical?:

Mechanical Kit will be shipped to you and you can learn and build using tutorials. You can start for free today!

1. 3D Printer

2. Automobile Prototyping

3. CNC Machine using Arduino

4. Project Management with Primavera

Burger equation is derived from the Navier Stokes equations by eliminating the effect of viscous, heat conduction and assuming that there is no temperature difference between fluid and surrounding in a fluid flow. In this project, you are going to solve a fluid flow problem using Lax Friedrich scheme.

Problem Description:

In a one dimension fluid flow problem, the length of the pipe is 1 meter. U is any conserved variable of the flow which is transporting at a speed of 12m/s. The value of U is -1.0unit from 0mm to 0.33mm and 0.66mm to 1.0mm. Find out the value of U in the domain at time t=2.0 sec assuming the flow to be inviscid, no conductive heat transfer and constant pressure throughout the flow.

Project Description:

  1. Burgers Equation: Burgers equation is a quadratic differential equation which is derived from the legendary Navier-Stokes equation.
  2. ?u/?t+?g(u)/?x=0

    Where, g(u)= u^2/2

  3. Finite Volume Method (FVM): The finite volume method is a method for representing and evaluating the partial differential equation in the form of algebraic equations. Here finite volume (cell) refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume integrals in a partial differential equation that contains divergence terms are converted to surface integrals using Gauss divergence theorem. These terms are the evaluated as fluxes at the surfaces of each finite volume. These are conservative in nature since the amount of flux leaving a surface is equal to the amount of flux entering into the finite volume.
  4. Lax Friedrich’s scheme: Several schemes are implemented on the basis of the finite volume method, one of which is Lax Friedrich’s scheme. To avoid the dependency of the solution on the direction of information flow, a central solver can be preferred. Lax-Friedrich’s scheme is one of the central solvers which can be used to solve a flow problem. Use Local Lax-Friedrich scheme for a better result.

Latest projects on Mechanical

Want to develop practical skills on Mechanical? Checkout our latest projects and start learning for free

Project Implementation:

  1. At first, learn basic of numerical methods. Learn how FVM is different from other methods, what is a node, discretization, errors in numerical methods, truncation error, stability and convergence.
  2. Then, learn what are the limitations in using FDM as a numerical approach to solve the differential equation.
  3. Find the Numerical solution to that equation using Lax-Friedrich’s scheme. In this step, you have to write codes to discretize the domain, initial the boundary condition and interact the solution for the number of times until you get an accuracy of 10e-5 and achieve timestep 1s. Don’t forget to save the result data in a text file. Solve for both the direction of flow.
  4. Then solve the same problem using Local Lax-Friedrich’s scheme.
  5. Plot the result data using Gnuplot or Minitab.
  6. Compare both the result and observe the difference.

Project Brief: By observation you can see, use of FVM is independent of the direction of information flow and produces a fairly approximate solution. You can also see that Local Lax-Friedrich’s scheme produces the more accurate result then Lax-Friedrich’s scheme.

Software requirements:

  1. Dev-C++: You will be needing Dev-C++ software to write logic and interact the solution for a number of times.
  2. Gnuplot: Also, you will be needing plotting software such as Gnuplot to plot the result data and compare the solution.

How to build Mechanical projects Did you know

Skyfi Labs helps students learn practical skills by building real-world projects.

You can enrol with friends and receive kits at your doorstep

You can learn from experts, build working projects, showcase skills to the world and grab the best jobs.
Get started today!

Programming language: C programming language

Kit required to develop Understanding FVM(Lax Friedrich scheme) by solving Burger equation:
Technologies you will learn by working on Understanding FVM(Lax Friedrich scheme) by solving Burger equation:
Understanding FVM(Lax Friedrich scheme) by solving Burger equation
Skyfi Labs Last Updated: 2022-04-18

Join 250,000+ students from 36+ countries & develop practical skills by building projects

Get kits shipped in 24 hours. Build using online tutorials.

More Project Ideas on Mechanical

Mechanical Foot Step Power Generator
Gearless Transmission Using Elbow Mechanism
Freedom WheelChair
Pneumatic Braking System
Automatic Braking Systems for Automobiles
Energy Glider
Water Jet Cutting Tool
Design and fabrication RC speedboat
Abrasive Jet Machine
Radio-Controlled Flying Wing
Autonomous fixed wing (drone)
Smartphone Controlled Paper Plane
Smartphone Controlled Paper Plane
Solar Endurance Flight
Smart Power Shoe
How to Develop an RC Ornithopter
Gesture Controlled Drone
Hybrid Drone
Voice Controlled Drone
Ocean Drone
Saucer Solar Drone
Car Copter
Electric Balloon Car
RC Helicopter
Homework Writing Machine with Arduino and Servo Motor
Mini Refrigerator
Hard water converter
Sterling Engine Helicopter
Eco Cooler
EL-bow mechanism – Gearless Transmission System
Everything you need to know about mercury vortex engines
Bucky paper Technology
Cryogenic grinding
Magnetic Bearing
Zero Turn Drives
Hyper loop
Laser Ignition System
Transformer Humanoid Automobile
Zero gravity 3D printer
2 Stroke Electric engines
Shape Memory Effect–Intelligent Alloys
3D Bio-printing Technology
Rail Gun
How to select the bldc motor for multicopter
5th Wheel Car Parking System
Gauss Accelerator
Electromagnetic Hover Car
Plasma Propulsion
Plasma Rail Gun
Light Gas Gun
Space Gun
Pneumatic Vulcanizing Machine
CNC Machine using Arduino
Mini Peltier Based Cooler
A Numerical Solution to One-Dimensional Euler equation, Shock tube Problem
A Numerical Solution to 2D Flat Plate Problem with Constant Conductivity Heat Transfer
Design of Water Quality Monitoring System using MSP430
3D printing using DLP Projectors
Black Box for RC Aircrafts
Electromagnetic Engines for Transportation
Glass Hybrid Fibres Epoxy Composite Material using Hand Layup Method
Vortex Bladeless Turbines
Manufacturing of MEMS
Automatic Pneumatic Paper Cutting Machine
Design and Fabrication of Automated Portable Hammering Machine
A Numerical Solution to Quasi-One-Dimensional Nozzle
A Numerical Solution to One Dimensional Conductive Heat Transfer with Constant Conductivity
A Numerical solution to One Dimensional Conductive Heat Transfer with Variable Conductivity
A Numerical Solution to Two-Dimensional Variable Conductivity Heat Transfer
Domestic Thermal Insulation with Sugarcane Composite
Understanding The Finite Difference Method by Solving Unsteady Linear Convection Equation
Understanding FVM(Lax Friedrich scheme) by solving Burger equation
Fabrication of Fiber reinforced composite material from Bamboo, Flex and Glass Fiber
A Numerical Study on Different Types of Fins
Microstructure and Thermal (TGA & DTA) Analysis of a Polymer Based Composite Material
Project on Pressure Drop Analysis in a Capillary Tube
Numerical Solution and Visualization of Two Blast Wave Interaction
Pedal Operated Water Pump
Analysis of Turbulence in a Two Dimensional Cavity Flow
Gas Detection System
Designing of Hydrogen Fuel car
Electromagnetic Shock Absorbers
Soap Free Building Sealant
Innovative Ground Storage
Dynamic Study of Soil Parameters
Centrifugal Pump
Self Priming Centrifugal Pump
Turbo Pump
Axial Flow Pump
Diaphram Pump
Plasma Ignition
Ram Accelerator
Aluminium Powered Car
Perpendicular Wind Turbines
Electromagnetic propulsion System
Miniature Shiftless Transmission
3D Printed Etching Press
Portable Loom
Hypnotic Plotter
Reconnaissance Drone
3D Printed DNA extractor
Health Monitoring Drone
Forward swept wing RC aircraft
Laser Propulsion
Repair of carbon composites
Quadrotor using Arduino
Drone Swarm
Cylinder-shaped Coaxial Drone
Drone-hunting Drone
Racing Drone
Compressed Air Powered Drone
Window washing drone
Performance analysis of paraffin wax,bees wax and magnesium for hybrid rocket motor
Fabrication and testing of light weight composites for UAV
Unmanned Aerial Photography using Flying Robot
Underwater Turbines
Power Generation by Seebeck Effect
Application of drones in construction
Smart Photography Drone
Heat power economy
Project on Missile Detection and Automatic Destroy System
Production of biodiesel from silkworm pupae for aircraft use
Improvement of aircraft accident investigation through expert systems
Flow analysis over a cylinder using ICM CFD
Self Inflating Tyres
CFD Analysis of a car
RC Hovercraft using Arduino
Autonomous Racing Drone
Ducted Fan Drone
Airborne Virus detector (Corona,SARS,Flu)
Airborne wind energy generation using Aerostat

Subscribe to receive more project ideas

Stay up-to-date and build projects on latest technologies