ME 7310

Project 2 Convection-Diffusion PDE Due: Mon., Nov. 1, 2010 at 6:00 pm

Solve the convection-diffusion equation: ∂u ∂u ∂2u +a =α 2 ∂t ∂x ∂x describing the wave propagation inside a one-dimensional channel. In this equation: a = 2.5 m/s ; α = 0.005 m2/s ; f inal time = 0.2 s ; 0 ≤ x ≤ 1 m and it is subject to the initial condition:

and the boundary conditions:

  1.0 if x ≤ 0.2 0.5 if x = 0.2 u(x, 0) =  0.0 if x ≥ 0.2 u(0, t) = 1.0 m/s ; u(1, t) = 0.

The analytical solution is obtained as:    x − x0 − at 1 √ 1 + erf u(x, t) = 1 − ; x0 = 0.2 m 2 2 αt Use the following explicit schemes: 1. Finite-Volume: FTCS for both convection and diffusion 2. Finite-Volume: First order upwind for convection, FTCS for diffusion 3. Finite-Difference: FTCS for both convection and diffusion 4. Finite-Difference: First order upwind for convection, FTCS for diffusion 5. Finite-Difference: Lax-Wendroff for convection, FTCS for diffusion 6. Finite-Difference: MacCormack for convection, FTCS for diffusion Objectives: 1. Compare the solution from different schemes at different times.

ME 7310

2. For at least one of the schemes check the accuracy by increasing the resolution (i.e. decreasing ∆t, ∆x). 3. Discuss: which scheme is more accurate? which ones are more dissipative or dispersive? Hint: Check the stability criteria, the truncation error and the modified equation of each scheme to explain its behavior for different ∆x and ∆t values.

## Project 2 - GitHub

Use the following explicit schemes: 1. Finite-Volume: FTCS for both convection and diffusion. 2. Finite-Volume: First order upwind for convection, FTCS for ...

#### Recommend Documents

Project 4.3 - Project Proposal - GitHub
Nov 5, 2013 - software will find the optimal meet time for all users. This component is similar to the ... enjoy each others company! Existing Approaches:.

Project 4 - GitHub
Project 4. Vorticity-Stream F\rnction Method. Due: Mon., Dec. 6, 2010 at 6:00 pm. Consider the incompressible laminar flow in the plane channel shown below.

QR Reader Java Project - GitHub
QR Reader Java Project. Date: 4 July ... Open eclipse and click on File -> import -> General -> Existing projects into workspace as shown in fig. 2. ... Similarly fix problem of JRE system library if in ... ProjectFlow.pdf show complete flow of proje

PDF 2 - GitHub
css/src/first.less') .pipe(less()), gulp.src('./css/src/second.css') .pipe(cssimport()) .pipe(autoprefixer('last 2 versions'))) .pipe(concat('app.css')) .pipe(minifyCss()).

Operating Systems Homework #2 - GitHub
May 7, 2015 - #include ... unsigned int tick () { // get current time (msec) ... Repeat think-hungry-eating cycle during given execution time in secs.

CSCI 305 Homework 2 - GitHub
Feb 23, 2018 - Describe how Fortran common blocks work and give an example. What happens if two named common blocks with the same name contain different variables? What is the difference between a blank common and a named common? What does the linker

STRUCTURE and Problem #2 - GitHub
Feb 7, 2017 - Uses multi-locus genotype data to investigate population ... the data betwee successive K values ... For this project, analyzing Fst outlier loci.