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Lecture 13: Advanced Time-Variable Solutions

Explore advanced time-variable solutions in water quality modeling, covering implicit and explicit approaches and numerical dispersion stability. Derivation of methods, implementation ease, and error considerations are discussed.

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Lecture 13: Advanced Time-Variable Solutions

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

  2. Lecture 13 • Advanced time-variable solutions • Implicit approaches >1 unknown in ea. eqn. • Explicit approaches only 1 unknown in ea. eqn. Lecture 13

  3. derivation of methods not covered in this class know for this class Lecture 13 • Advanced time-variable solutions • Implicit approaches • Explicit approaches • Table 13.1 Lecture 13

  4. Numerical dispersion: Stability: FTCS explicit methods FTBS Recall from Lecture 12 Constraints: Finite difference approaches: Lecture 13

  5. Lecture 13 • Explicit method • MacCormack – CTCS • Implicit methods • BTCS • Crank-Nicholson Lecture 13

  6. Method Numerical dispersion Stability Implemen-tation Ease FTBS Easy FTCS Easy MacCormack CTCS None Conditional (more liberal) Moderate error inbook! BTCS Difficult Crank-Nicholson None Difficult Table 13.1 Lecture 13

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