| 5 | | ||'''February 8''' || || Greg || || || || || |
| 6 | | ||'''February 15''' || || Lauren || || Christine || || || |
| 7 | | ||'''February 22''' || || Dan || || Munier || || || |
| 8 | | ||'''March 1''' || || Jia || || Matt || || || |
| 9 | | ||'''March 8''' || || Yuan || || Miao || || || |
| 10 | | ||'''March 15''' || || Christine || || || || || |
| 11 | | ||'''March 22''' || || No meeting || || No meeting || || || |
| 12 | | ||'''March 29''' || || Munier || || || || || |
| 13 | | ||'''April 5''' || || Dan || || || || || |
| 14 | | ||'''April 12''' || || Ricardo || || Greg || || || |
| 15 | | |
| 16 | | ||'''April 19''' || || || || || || || |
| | 5 | ||'''February 8''' || || Greg || || || || Forms of the Euler equations |
| | 6 | ||'''February 15''' || || Lauren || || Christine || || Waves || |
| | 7 | ||'''February 22''' || || Dan || || Munier || || The Riemann Problem || |
| | 8 | ||'''March 1''' || || Jia || || Matt || || Conservation Principles || |
| | 9 | ||'''March 8''' || || Yuan || || Miao || || Domain of Influence || |
| | 10 | ||'''March 15''' || || Christine || || || || Stability || |
| | 11 | ||'''March 22''' || || No meeting || || No meeting || || No meeting || |
| | 12 | ||'''March 29''' || || Munier || || || || Basic Methods for Scalar Conservation Laws || |
| | 13 | ||'''April 5''' || || Dan || || || || Basic Methods for Euler equations || |
| | 14 | ||'''April 12''' || || Ricardo || || Greg || || Advanced Methods I || |
| | 15 | ||'''April 19''' || || || || || || Advanced Methods II || |
| | 20 | |
| | 21 | |
| | 22 | Topics (numbers refer to pages in Laney's Computational Gasdynamics unless otherwise indicated) |
| | 23 | |
| | 24 | 1. Forms of the Euler equations |
| | 25 | - Integral form (5-12) |
| | 26 | - Conservative (differential) form, weak vs. strong solutions (13-15) |
| | 27 | - Primitive form (16-17) |
| | 28 | |
| | 29 | 2. Waves |
| | 30 | - Scaler example (21-25) |
| | 31 | - Vector example, characteristics (26-27) |
| | 32 | - Characteristic form of the Euler equation (28-32) |
| | 33 | - Simple waves, expansion waves, compression/shock waves, contact discontinuities (37-45) |
| | 34 | - Waveform preservation, destruction and creation (64-68) |
| | 35 | |
| | 36 | 3. The Riemann Problem |
| | 37 | - RP for the Euler Equations (72-75) |
| | 38 | - RP for Linear Systems of Equations (75-82) |
| | 39 | - Three wave linear approximation (Roe's solver) (82-93) |
| | 40 | - One wave linear solver (94-95) |
| | 41 | - Two wave solvers: HLL, HLLE (Toro: 315-336) |
| | 42 | |
| | 43 | 4. Conservative Principles |
| | 44 | - Conservative Finite-Volume Methods and shock location (187-193) |
| | 45 | - forward time, backward-time, centered-time (194-202) |
| | 46 | - Conservative Finite-Difference connection (203-205) |
| | 47 | |
| | 48 | 5. Domain of Influence |
| | 49 | - Upwinding introduction (222-226) |
| | 50 | - Flux averaging (228-230) |
| | 51 | - Flux splitting (231-237) |
| | 52 | - Reconstruction-Evolution methods (intro) (243-247) |
| | 53 | |
| | 54 | 6. Stability |
| | 55 | - Linear stability (256-261) |
| | 56 | - Nonlinear stability (272-275) |
| | 57 | - monotonicity (276-277) |
| | 58 | - TVD (277-282) |
| | 59 | |
| | 60 | 7. Basic Methods for Scalar Conservation Laws |
| | 61 | - Introduction/test cases (309-312) |
| | 62 | - Artificial viscosity (249-252) |
| | 63 | - Lax-Wendroff (316-322) |
| | 64 | - Gudonov's First-Order Upwind scheme (323-329) |
| | 65 | |
| | 66 | 8. Basic Methods for Euler equations |
| | 67 | - Overview of Methods: Flux vs. Wave approaches (351,355, 362) |
| | 68 | - Reconstruction-Evolution (406-410) |
| | 69 | - multidimensions (602-603) |
| | 70 | |
| | 71 | 9. Advanced Methods |
| | 72 | - Flux-limited methods (459-463), Van Leer's method (464-465) |
| | 73 | - Flux-corrected methods (504-506), FCT (507-514) |
| | 74 | - Reconstruction-Evolution Methods (565), MUSCL (565-573), PPM (574-577) |
| | 75 | |
