MATH 592 Home Page

• Wednesday, 15
  Discuss research projects
• Friday, 17
  1-D, inviscid Euler equations
  Project #1 Assigned
  
  
  

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• Monday, 20
  No class - holiday
  
• Wednesday, 22
  2-D, inviscid Euler equations
  Linearized methods for the 1-D, inviscid Euler equations
  
• Friday, 24
  Linearized methods for the 1-D, inviscid Euler equations
  Linearized methods for the 2-D, inviscid Euler equations
  
  
  

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• Monday, 27
  1-D Isentropic and 1-D isothermal equations
  
• Wednesday, 29
  1-D shallow water equations
  Classification of the 1-D shallow water equations
  Classification of the 1-D isothermal equations
  
• Friday, 31
  Classification of the 1-D isentropic equations
  Classification of the 1-D Euler equations
  
  
  

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• Monday, 3
  Classification of the 2-D Euler equations
  Simultaneous diagonalization of the 2-D Euler equations
  
• Wednesday, 5
  Characteristics for scalar, nonlinear conservation laws
  Constant solutions along characteristics for scalar, nonlinear conservation laws
  
• Friday, 7
  Breaking point
  Characteristics for the inviscid Burgers' equation
  Weak solutions
  
  
  

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• Monday, 10
  Weak solutions
  Weak solutions and classical solutions
• Wednesday, 12
  Preliminary Project Presentations
  Project #1 Due
  
• Friday, 14
  Preliminary Project Presentations
  
  
  

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• Monday, 17
  No class - holiday
  
• Wednesday, 19
  Preliminary Project Presentations
  Discontinuous solutions
  Speed of propagation of discontinuous solutions
  
• Friday, 21
  The Rankine-Hugoniot or jump condition for weak solutions
  
  
  

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• Monday, 24
  Using the jump condition to construct discontinuous weak solutions
  The vanishing viscosity solution
  
• Wednesday, 26
  Entropy Condition I
  Entropy Condition I for nonconvex functions
  Entropy Conditions and uniqueness
  Entropy Condition II
  
• Friday, 28
  Conservation of entropy
  Entropy and entropy flux functions
  Entropy Condition III
  
  
  

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• Monday, 3
  Examples with Entropy Condition III
  The Riemann problem
  
• Wednesday, 5
  Similarity solutions
  
• Friday, 7
  Systems of conservation laws
  Genuinely nonlinear and linearly degenerate conservation laws
  
  
  

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• Monday, 10
  m-characteristics
  Nonlinear characteristic curves
  Entropy Condition I for systems
  k-shocks
  
• Wednesday, 12
  Entropy Condition III for systems
  The Riemann problem for systems
  
• Friday, 14
  Discussion concerning projects
  
  
  

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• Monday, 17
  No class - holiday
  
• Wednesday, 19
  No class - holiday
  
• Friday, 21
  No class - holiday
  
  
  

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• Monday, 24
  The Riemann problem for the 1-D Euler equations
  Constant states for the 1-D Euler equations
  
• Wednesday, 26
  Classification of m-characteristics for the 1-D Euler equations
  
• Friday, 28
  The fan, the contact discontinuity, and the shock for the 1-D Euler equations
  
  
  

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• Monday, 31
  Sample numerical results for the inviscid Burgers' equation
  Conservative Lax-Wendroff for the 1-D Euler equations
  

• Wednesday, 2
  Numerical schemes for general nonlinear conservation laws
  Nonlinear pointwise consistency
  Nonlinear norm consistency
  
• Friday, 4
  Conservative difference schemes for general nonlinear conservation laws
  Numerical flux function
  
  
  

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• Monday, 7
  Consistency of conservative difference schemes
  Lax-Wendroff Theorem
  
• Wednesday, 9
  Summation form of conservation laws
  Numerical entropy flux function
  Discrete Entropy Condition III and vanishing viscosity solutions
• Friday, 11
  Numerical entropy flux functions for FTBS in both the linear and nonlinear case
  E schemes
  Monotone schemes
  
  
  

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• Monday, 14
  Total Variation Diminishing (TVD) schemes
  Essentially Nonoscillatory (ENO) schemes
  Linear Lax-Wendroff is not monotone
  Nonlinear Lax-Friedrichs is monotone
  
• Wednesday, 16
  Linear FTBS is not TVD
  Linearized Lax-Wendroff is not TVD
  Incremental form (I-form) of a difference scheme
  Q-form of a difference scheme
  
• Friday, 18
  No class - Make-up for Tafti visit
  
  
  

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• Monday, 21
  No class - Make-up for Tafti visit
  
• Wednesday, 23
  Theory of E schemes
  
• Friday, 25
  Theory of monotone schemes
  Theory of TVD schemes
  Incremental TVD schemes
  
  
  

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• Monday, 28
  The Godunov method
  
• Wednesday, 30
  The Godunov method
  High resolution schemes
  

• Friday, 2
  Flux-limiter methods
  
  
  

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Homework and projects

Project #1 Due Wednesday 2-12

Preliminary Project Presentations Wednesday 2-12

Project Presentations Thursday 3-13

Written Project Proposals Due Friday 3-28

Final Project Presentations Tuesday 5-6

Written Project Reports Due Wednesday 5-7

Software