1. CE 498/698 and ERS 685 (Spring 2004) Lecture 131 Lecture 13: Advanced Time- Variable Solutions CE 498/698 and ERS 685 Principles of Water Quality Modeling

2. CE 498/698 and ERS 685 (Spring 2004) Lecture 132 Advanced time-variable solutions –Implicit approaches >1 unknown in ea. eqn. only 1 unknown in ea. eqn. –Explicit approaches

3. CE 498/698 and ERS 685 (Spring 2004) Lecture 133 Advanced time-variable solutions –Implicit approaches –Explicit approaches derivation of methods not covered in this class know for this class Table 13.1

4. CE 498/698 and ERS 685 (Spring 2004) Lecture 134 Recall from Lecture 12 Constraints: Numerical dispersion: Stability: Finite difference approaches: FTCS FTBS explicit methods

5. CE 498/698 and ERS 685 (Spring 2004) Lecture 135 Explicit method –MacCormack – CTCS Implicit methods –BTCS –Crank-Nicholson

6. CE 498/698 and ERS 685 (Spring 2004) Lecture 136 DifficultNone Crank- Nicholson DifficultBTCS ModerateConditional (more liberal)None MacCormack CTCS EasyFTCS EasyFTBS Implemen- tation Ease Stability Numerical dispersion Method Table 13.1 error in book!