INSTITUTE OF PHYSICS PUBLISHING Nonlinearity 18 (2005) R1R16
NONLINEARITY doi:10.1088/0951-7715/18/5/R01
INVITED ARTICLE
A general method for conserving quantities related to potential vorticity in numerical models
Rick Salmon
Scripps Institution of Ocean

MPO 662 Problem Set 3
1
Implicit multi-step methods
The third-order Adams Moulton method uses the time-levels tn+1 , tn , and tn1 to interpolate
the right hand side function f to third-order accuracy using quadratic polynomials. Derive
the coecients ai of

MPO 662 Problem Set 3
It is very important that you discuss the numerical results you produce, particularly if they conform with your expectation about what the solution should look like, and if not what may have caused the problems. Plots with no discuss

MPO 662 Problem Set 4
Abstract The aim of this homework is to perform an in-depth analysis of the energy conserving discretization of the shallow water equation presented in class. The analysis centers on the continuous and discrete equations, and a worki

MPO 662 Problem Set 4 1 Consistency and stability
You have reverse-engineered a computer program and deciphered that it updates the variable u according to the following rule: 3un - 4un + un un+1 - un j j-2 j-1 j +c j =0 (1) t 2x Determine the continuous

MPO 662 Problem Set 4
1. The Lax-Wendroff method replaces time-derivatives with spatial derivatives and the latter are approximated with centered differences. An alternate algorithm known as the Warming and Beam (Tannehill et al. , 1997; Durran, 1999) rep

MPO 662 Problem Set 5
1. numerical gravity wave dispersion The tide propagation inside a channel is simulated using a finite difference model. The user is trying to decide how to configure it. Use the dispersion relationship to decide on the number of poi

MPO 662 Problem Set 5
The pupose of this homework is to write a one-dimensional shallow water solver using second-order schemes that can be viewed as either finite difference methods or finite volume methods, the discrete equations being the same. An impo

MPO 662 Problem Set 6
Abstract The aim of this homework is to perform an in-depth analysis of the energy conserving discretization of the shallow water equation presented in class. The analysis centers on the continuous and discrete equations, and a worki

MPO 662 Problem Set 6
Abstract The aim of this homework is to perform an in-depth analysis of the energy conserving discretization of the shallow water equation presented in class. The analysis centers on the continuous and discrete equations, and a worki

MPO 662 Problem Set 3
1
Hyperbolic equations
. Consider the Lax Fredrichs approximation to the scalar advection equation:
un
+un
un+1 un1
un+1 j+1 2 j1
j
j
j
+c
=0
t
2x
Determine the truncation error for this scheme
Study the consistency of this FD repr

MPO 662 Problem Set 4
1
Consistency and stability
You have reverse-engineered a computer program and deciphered that it updates the variable
u according to the following rule:
3un 4un1 + un2
un+1 un
j
j
j
j
+c j
=0
t
2x
(1)
Determine the continuous PDE t

MPO 662 Problem Set 1
Feel free to use symbolic computation software such as mathematica or the symbolic toolbox in matlab to carry out the algebra 1. Find the characteristics of the following PDEs (a) uxx + 3uxy + uyy = 0 (b) uxx 2uxy + uyy = 0 2. Consid

2016
JOURNAL OF THE ATMOSPHERIC SCIENCES
VOLUME 61
Poisson-Bracket Approach to the Construction of Energy- and Potential-EnstrophyConserving Algorithms for the Shallow-Water Equations
RICK SALMON
Scripps Institution of Oceanography, University of Californ

Journal of Computational Physics 160, 318335 (2000) doi:10.1006/jcph.2000.6465, available online at http:/www.idealibrary.com on
Incremental Remapping as a Transport/ Advection Algorithm
John K. Dukowicz and John R. Baumgardner
Theoretical Division, Los A

C OMMUNICATIONS O N P URE AND APPLIED M ATHEMATICS, \'OL. IX,
267-293 (1956)
Survey of the Stability of Linear Finite Difference Equations*
P. I>. L A X and R. D. R ICHTMYEK
P ART I A N EQUIVALENCE THEOREM
1. I ntroduction
Beginning with the discovery by

46
CHAPTER 3. FINITE DIFFERENCE APPROXIMATION OF DERIVATIVES
3.5
Compact Dierencing Schemes
A major disadvantage of the nite dierence approach presented earlier is the widening
of the computational stencil as the order of the approximation is increased. T

MPO 662 Problem Set 1
Feel free to use symbolic computation software such as mathematica or the symbolic
toolbox in matlab to carry out the algebra
1. Classify the following PDEs
(a) utt + uxx + ux = ekt
(b) uxx uxy + uy = 4
2. Find the characteristics of

MPO 662 Problem Set 1
Feel free to use symbolic computation software such as mathematica or the symbolic
toolbox in matlab to carry out the algebra. See 1 to see an example with matlab.
1
Finite Dierence Derivation
Use Taylor series to derive explicit nit

MPO 662 Problem Set 2
Feel free to use symbolic computation software such as mathematica or the symbolic
toolbox in matlab to carry out the algebra. See 1 to see an example with matlab.
1. Use Taylor series to derive explicit nite dierence approximations

Chapter 7
Numerical Dispersion of Linearized SWE
This chapter is concerned with the impact of FDA and variable staggering on the fidelity of wave propagation in numerical models. We will use the shallow water equations as the model equations on which to c