New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Numer Simul in WeatherClimate

by: Verna Brekke

Numer Simul in WeatherClimate CLIM 715

Marketplace > George Mason University > Climate Dynamics > CLIM 715 > Numer Simul in WeatherClimate
Verna Brekke
GPA 3.76

Paul Schopf

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Paul Schopf
Class Notes
25 ?




Popular in Course

Popular in Climate Dynamics

This 17 page Class Notes was uploaded by Verna Brekke on Monday September 28, 2015. The Class Notes belongs to CLIM 715 at George Mason University taught by Paul Schopf in Fall. Since its upload, it has received 35 views. For similar materials see /class/215044/clim-715-george-mason-university in Climate Dynamics at George Mason University.

Similar to CLIM 715 at Mason

Popular in Climate Dynamics


Reviews for Numer Simul in WeatherClimate


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/28/15
Diffusion Durran 34 Prototype Problem LIP M6211 at W This is a dissipative operator as we discussed previoust Mk at w Forward scheme conditionally stable Leapfrog unconditionally unstable Trapezoidal unconditionally stable LeapFrog Scheme for dipdt K11 n1 pm 1 Write ampli cation factor for q An A2 1 2mm A KAZI V1Ar2K2 negative choice givesA lt Forward Step n1 n n n n qu qu Mqgtj1 2 qu A15 A5232 recall 311 311 2 COS kAm 1 0 1 I2vIcoskAx so If we use Z A Z A1 2v1 coskAx where VMAtAx2 O 1 4V 1 O n Stability Criterion O s v 5 V2 Features of Forward Scheme 0 If v gt Mr then shortest waves oscillate while damping 0 Stability requires that At decrease faster than Ax so that high resolution leads to trouble 0 Errors in short waves are damped so perhaps we do not need to have high accuracy ie they all go to O Implicit If we use an implicit scheme for diffusion we can obtain a scheme that is unconditionally stable even if it tends to damp the shortest waves more quickly than nature WH WM At 2 MAI 2 n 1 MAI 2 n lt1 axgt w ax 63 ill5i 2 2 CrankNicholson Method 1 MTm i 4 1A4Tm63 Convert to wavenumber space reorganize MAI n MAI n 1 EcoskAx 1 k 1EcoskAx 1 k 1 v1 coskAx 1v1 coskAx k lt1 Unconditionally sable Practical Considerations 0 Implicit differencing is easy in ld more dif cult in 2d 0 Used commonly for vertical mixing in ocean models 0 Tridiagonal solvers quite ef cient Thomas Tridiagonal Algorithm aixi1 bixi Cixi l di Try xiEixi1Fi aixi1 bixi CiEi lxi di CiE l x aix 1 1 biCiEi 1 1 biCiEi 1 V V SO Ei F E aquot biciEi1 Solve for EF for i I2N di CiFi l i m then XI for iN NI I Advection and Diffusion aw aw 62w M at C ax 6x2 Consider just horizontal differencing and try upstream for advection centered for diffusion 0 E 05x j 12 M iqh Recall that the upstream advection is diffusive can we combine Modi ed Equation Look at the modi ed equation the upstream term looks like 81p chazxp 6x C 1 12 Cax 2 8x2 so our equation is an approximation to a a Ax 82 w lt C gt w M 1 at Cax 2M 6x2 81p 81p P6 8211 M 1 6tcax 2ax2 P6g M Pe ratio of advective to diffusive effects In theory UL M Pe where L is the length scale of the problem U is the velocity scale and M is the diffusivity For momentumthe equivalent is the Reynolds number Re ULv In our case the length scale L is replaced by AX so we are measuring the Peclet or Reynolds number at the nest grid resolution The error is proportional to the numerical Peclet number and we need Pe ltlt With coarse resolution and high flow velocity our solutions have too much numerical diffusion Solutions of arti cially increasing M to decrease Pe do not help If the true solution has M and we use M1 MAM our modi ed equation is 2 w w new a w M atlcax M 2 6x2 Stablilty Fourier transformed version of the original equation ZIP 2 dtzck1p Mklp d1p dt zu1pMp where u and k are real and k lt O The true solutions all have 1pt s 1p0 Differencing Schemes Forward LeapFrog 11imAtxAt Az XibA10 For any amount of diffusion leapfrog is unstable Hybrid n1 pm 1 n A n l 2A2 mp 4 LF Forward A22iaA12X Aibi127x I2 V L Combined SpaceTime Analysis So far we have considered space differencing with perfect time differencing and time differencing with perfect space differencing Forward time centered space 6t 2 cazxcb M634


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Amaris Trozzo George Washington University

"I made $350 in just two days after posting my first study guide."

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.