Simulations Seminar Schedule

Meetings will be held Fridays from 2:30-3:30 in Pupin 1402


Date Leader 1 Leader 2 Topic
February 8 (3pm this week only) Greg Forms of the Euler equations
February 15 Lauren Christine Waves
February 22 Dan Munier The Riemann Problem I
March 1 Ricardo Matt The Riemann Problem II
March 8 Yuan Miao Conservation Principles
March 15 Christine Greg Domain of Influence
March 22 No meeting No meeting No meeting
March 29 Munier Jeff Stability
April 5 Dan Aleksey Basic Methods for Scalar Conservation Laws
April 12 Ricardo Greg Basic Methods for Euler equations
April 19 NO MEETING (Bishop Lecture)
April 26 Cancelled
May 3 NO MEETING (Big Apple colloquium)
May 10 Greg Advanced Methods

Topics (numbers refer to pages in Laney's Computational Gasdynamics unless otherwise indicated)

Electronic version of text can be accessed through the library website: http://clio.cul.columbia.edu:7018/vwebv/holdingsInfo?bibId=9445777

1. Forms of the Euler equations

  • Integral form (5-12)
  • Conservative (differential) form, weak vs. strong solutions (13-15)
  • Primitive form (16-17)

2. Waves

  • Scaler example (21-25)
  • Vector example, characteristics (26-27)
  • Characteristic form of the Euler equation (28-32)
  • Simple waves, expansion waves, compression/shock waves, contact discontinuities (37-45)
  • Waveform preservation, destruction and creation (64-68)

3. The Riemann Problem

  • RP for the Euler Equations (72-75)
  • RP for Linear Systems of Equations (75-82)
  • Three wave linear approximation (Roe's solver) (82-93)
  • One wave linear solver (94-95)
  • Two wave solvers: HLL, HLLE (Toro: 315-336)

4. Conservative Principles

  • Conservative Finite-Volume Methods and shock location (187-193)
    • forward time, backward-time, centered-time (194-202)
  • Conservative Finite-Difference connection (203-205)

5. Domain of Influence

  • Upwinding introduction (222-226)
  • Flux averaging (228-230)
  • Flux splitting (231-237)
  • Reconstruction-Evolution methods (intro) (243-247)

6. Stability

  • Linear stability (256-261)
  • Nonlinear stability (272-275)
    • monotonicity (276-277)
    • TVD (277-282)

7. Basic Methods for Scalar Conservation Laws

  • Introduction/test cases (309-312)
  • Artificial viscosity (249-252)
  • Lax-Wendroff (316-322)
  • Gudonov's First-Order Upwind scheme (323-329)

8. Basic Methods for Euler equations

  • Overview of Methods: Flux vs. Wave approaches (351,355, 362)
  • Reconstruction-Evolution (406-410)
  • multidimensions (602-603)

9. Advanced Methods

  • Flux-limited methods (459-463), Van Leer's method (464-465)
  • Flux-corrected methods (504-506), FCT (507-514)
  • Reconstruction-Evolution Methods (565), MUSCL (565-573), PPM (574-577)