| Monday |
Wednesday |
Friday |
| Mar 30 Introduction to Scalar Hyperbolic Equations:
Derivation
Definition of hyperbolic equations
|
Apr 1
Linear Advection Equation,
Burger Equation,
Method of Characteristics
Domain of dependence
Range of Influence
Weak Solution
|
Apr 3
Numerical Method:
1st Order Upwind
|
| Apr 6
Numerical Method:
Lax-Wendroff
2nd Upwind
for u_t+ a u_x = 0
ENO for u_t + a u_x = 0
Lax-Friedrich Scheme
HW1
|
Apr 8
Riemann Problem
Shock speed
|
Apr 10
Entropy Conditions for Discontinuity
|
| Apr 13
Entropy Condition based on the spreading of characteristics
HW2 |
Apr 15
Manipulating Conservation Laws
Entropy Functions |
Apr 17
Some Scalar Example:
Traffic Flow
Sound Speed
|
|
Apr 20
Two Phase Flow
Shallow Water Eqns
HW3 |
Apr 22
Numerical Method for Linear System Equations
Backward Euler, Lax-Friedrichs, Lax-Wendroff, and Upwind
|
Apr 24
Local Truncation Error
Stability
The Lax Equivalence Theorem
|
| Apr 27 Conservative Methods for Nonlinear Problems |
Apr 29
Consistency
HW4
|
May 1
Discrete Conservation
|
| May 4
The Lax-Wendroff Theorem
|
May 6
Godunov's Method
HW5 |
May 8
Discrete entropy condition
|
| May 11
Compactness |
May 13
Total variation stability
HW6 |
May 15
l_1-contracting numerical methods |
| May 18
Monotone methods |
May 20
Higher Order Scheme HW7 |
May 22
flux limiter |
| May 25
Memorial Day: no class |
May 27
slope limiter |
May 29
slope limiter for nonlinear eqnationHW8 |
| Jun 1
2D simulation |
Jun 3
Central Scheme and Spectral Difference |
Jun 5 ENO, WENO,
Spectral Volume, DG |
| Jun 8
Final Presentation: 11:30pm-1:18pm
Final Exams week |
Jun 10 Final Exams Week |
Jun 12
Final Exams Week
|
| |
|
|
