| Monday |
Wednesday |
Friday |
| Mar 28 Introduction to Scalar Hyperbolic Equations:
Derivation
Definition of hyperbolic equations
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Mar 30
Linear Advection Equation,
Burger Equation,
Method of Characteristics
Domain of dependence
Range of Influence
Weak Solution
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Apr 1
Numerical Method:
1st Order Upwind
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| Apr 4
Numerical Method:
Lax-Wendroff
2nd Upwind
for u_t+ a u_x = 0
ENO for u_t + a u_x = 0
Lax-Friedrich Scheme
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Apr 6
Riemann Problem
Shock speed
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Apr 8
Entropy Conditions for Discontinuity
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| Apr 11
Entropy Condition based on the spreading of characteristics
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Apr 13
Manipulating Conservation Laws
Entropy Functions |
Apr 15
Some Scalar Example:
Traffic Flow
Sound Speed
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Apr 18
Two Phase Flow
Shallow Water Eqns
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Apr 20
Numerical Method for Linear System Equations
Backward Euler, Lax-Friedrichs, Lax-Wendroff, and Upwind
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Apr 22
Local Truncation Error
Stability
The Lax Equivalence Theorem
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| Apr 25 Conservative Methods for Nonlinear Problems |
Apr 27
Consistency
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Apr 29
Discrete Conservation
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| May 2
The Lax-Wendroff Theorem
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May 4
Godunov's Method
| May 6
Discrete entropy condition
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| May 9
Compactness |
May 11
Total variation stability
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May 13
l_1-contracting numerical methods |
| May 16
Monotone methods |
May 18
Higher Order Scheme |
May 20
flux limiter |
| May 23
2D simulation |
May 25
slope limiter |
May 27
slope limiter for nonlinear eqnation |
| May 30
Memorial Day: no class |
Jun 1
Central Scheme and Spectral Difference |
Jun 3 ENO, WENO,
Spectral Volume, DG |
| Jun 6
Final Presentation: 11:30am-1:18pm
Final Exams week |
Jun 8 Final Exams Week |
Jun 10
Final Exams Week
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