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UCSB
CS 111  Introduction to Scientific Computing
Final Project 3  Due on the ﬁnal exam day at 5pm
You are not allowed to work in group for the ﬁnal project.
The goal of this project is to implement the NavierStokes equations in two spatial dimensions.
The velocity ﬁeld
U
= (
u,v
) is given by:
U
t
+ (
U
· ∇
)
U
=
∇
p
+
μ
∇
2
U
+
F,
with
∇ ·
U
= 0
.
Here
p
is the pressure,
F
= (
f
1
,f
2
) is an external force and
μ
=
.
001 is the viscosity coeﬃcient.
1. What are the boundary conditions for the velocity at the walls?
2. Write down the main step of the projection method.
3. Write down the linear system associated with the discretization of the viscosity term. What are
the boundary conditions?
4. Write down the linear system associated with imposing the incompressibility constraint. What
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This note was uploaded on 12/29/2011 for the course CS 111 taught by Professor Staff during the Fall '08 term at UCSB.
 Fall '08
 Staff

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