Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
1
Solution 3 April 19, 2012
CEE262c Solution 3:
1D Shallow water equation solver
Due: In class Thursday, May 3, 2012
In this assignment you will study the behavior of the 1d verticallyaveraged shallow water
equations,
h
+
(Hu) = 0 ,
t
x
u
h xs Cd u
u
Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
1
Solution 2 April 10, 2012
CEE262c Solution 2:
Advection schemes
Due: In class Thursday, April 19, 2012
For this assignment you will implement a TVD advection scheme to compute advection of
a passive tracer in one and two dimensions. Begining with the tw
Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
1
Solution 6 May 31, 2012
CEE262c Solution 6:
Straininduced periodic stratification (SIPS)
Due: Thursday, June 12, 2012
Estuarine dynamics are strongly dominated by the interaction of fresh, buoyant river water
with salty, heavy sea water. During the flo
Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
1
Solution 1 April 3, 2012
CEE262c Solution 1:
Finite differences and order of accuracy
Due: In class Tuesday, April 10, 2012
1. Derive the fourpoint onesided finite difference approximation to the first derivative
and determine the form of the leading
Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
1
Solution 4 May 8, 2012
CEE262c Solution 4:
Numerical dispersion
Due: In class Thursday, May 17, 2012
Numerical discretization of the linearized shallow water equations can be analyzed by discretizing the unidirectional wave equation for the free surface
Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
CEE 262A
HYDRODYNAMICS
Lecture 2
Mathematical preliminaries and tensor
analysis
1
Righthanded, Cartesian coordinate system
z x3
x
a
~
3
a2
a
1
Unit vectors
y x2
x x1
a1 (1,0,0) i
a 2 (0,1,0) j
a 3 (0,0,1) k
Position vector
x a1 x1 a 2 x2 a 3 x3
~
Where (
Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
1
Solution 5 May 17, 2012
CEE262c Solution 5:
2D (xz) Linearized nonhydrostatic solver
Due: In class Thursday, May 31, 2012
In this assignment you will implement a discretization of the linearized nonhydrostatic equations of motion and show that the dis
Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
CEE 262A
HYDRODYNAMICS
Lecture 4
Kinematics Part II
1
Stream Function
(a) We will show that if conservation of mass (continuity) is:
1 D ui
Dt xi
Then for an incompressible or slightly compressible fluid
D
0
Dt
ui
0
xi
or u 0
~
A
u f ( x3 ) or u f ( z )
Modeling and Simulation for Civil and Environmental Engineers
CEE 262C

Spring 2014
CEE 262A
HYDRODYNAMICS
Lecture 1*
Introduction and properties of fluids
*Adapted from notes by Prof. Stephen Monismith
1
The NavierStokes equation
2
What is a Fluid ? (Fluid vs. Solid)
A substance which deforms continuously under the
action of a shearin