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		Matt				Advanced Methods I
April 26		Jeff				Advanced Methods II
May 3
May 10

---

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)