# Day05-slides - 1 Atms 502 CS 505 CSE 566 Numerical Fluid...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Atms 502 CS 505 CSE 566 Numerical Fluid Dynamics Thu., 7 September 2006 9/29/06 Atms 502 - Fall 2006 2 2 ∆ x grows fastest.. Amplification factor: Stability analysis: Say σ = 1. Then: Plug in: " = 1 # 4 \$ sin 2 k % x 2 & ’ ( ) * + " # " 1 2 " = 1 # 4sin 2 \$ 2 % & ’ ( ) * L = " # \$ = 0 # % = 1 & 4(0) = 1 L = 4 ’ x # \$ = ( 2 # % = 1 & 4(0.5) = & 1 L = 2 ’ x # \$ = ( # % = 1 & 4( 1 ) = & 3 stable stable unstable 9/29/06 Atms 502 - Fall 2006 3 Operator deFnitions Derivatives: Averaging: • Example: advection w/staggered grids: udT/dx " x f ( x ) = f i + 1/2 # f i # 1/2 \$ x ; " 2 x f ( x ) = f i + 1 # f i # 1 2 \$ x u x = u i + 1/2 + u i " 1/2 2 ; u 2 x = u i + 1 + u i " 1 2 u u T T T T T 9/29/06 Atms 502 - Fall 2006 4 wave forms You may have seen expressions such as these, describing wave motions: • Units of ω ? • What about x-ct? We’ll be considering the possibility of a complex frequency: So what? u = A cos( kx ) u = A cos[ k ( x " ct )] u = Ae ik ( x " ct ) u = Ae i ( kx " # t ) " = " r + i " i u = Ae i ( kx " # t ) \$ u = Ae i kx " # r + i # i ( ) t [ ] \$ u = Ae # i t ( ) e i kx " # r t ( ) Amplitude: Exponential growth? 2 9/29/06 Atms 502 - Fall 2006 5 Now look just at time dependence: This is of the form: The above is the oscillation equation Oscillation equation Start with the linear...
View Full Document

## This note was uploaded on 10/06/2009 for the course ATMOSPHERI 502 taught by Professor Jewett during the Spring '09 term at University of Illinois at Urbana–Champaign.

### Page1 / 4

Day05-slides - 1 Atms 502 CS 505 CSE 566 Numerical Fluid...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online