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Reservoir Convergence Algorithms: Current Methods in Solving Function Equations

Learn about the convergence algorithm used in reservoir functions, such as simultaneous equation solving. Explore the bisection algorithm for reservoir types, and its application in various scenarios.

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Reservoir Convergence Algorithms: Current Methods in Solving Function Equations

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  1. Reservoir Convergence Algorithms Convergence Algorithm Previously Used Current Convergence Algorithm

  2. Convergence algorithm used in functions that require the simultaneous solving of a set of 2 equations Bisection algorithm used in all reservoir types in getMaxOutflowGivenInflow getMaxReleaseGivenInflow getMinSpillGivenInflowRelease solveMB_givenInflowRelease General

  3. Example - getMaxOutflowGivenInflow outflow fMAX(stor,Q) QMAX,MB fMB(stor,Q) storMAX,MB storage

  4. 1. Simple Convergence Algorithm • Iterates by updating the dependent variable (outflow) based on the changing of the • independent variable (storage) outflow outflow fMAX(stor,Q) fMAX(stor,Q) fMB(stor,Q) fMB(stor,Q) storage storage Ideal Problematic

  5. Bisection Algorithm • Incremental search method where the interval is divided in half at each iteration outflow outflow QMBave fMAX(Q,stor) fMAX(Q,stor) QMAXave QMBave QMAXave fMB(Q,stor) fMB(Q,stor) stor_low stor_ave stor_high storage stor_low stor_ave stor_high storage stor_low stor_ave

  6. 2. Bisection Replaces Simple Algorithm • The simple algorithm was replaced with the bisection algorithm. This approach also • proved to be problematic. fMAX(Q,stor) outflow outflow fMAX(Q,stor) QMBave QMAXave fMB(Q,stor) fMB(Q,stor) stor_low stor_ave stor_high stor_low stor_high storage storage stor_low stor_ave Ideal Problematic

  7. 3. Current Algorithm - Combination of Simple & Bisection • If the simple convergence routine fails, the bisection routine is employed. • The last 4 points of the simple routine become the bisection routine’s starting points. outflow outflow fMAX(Q,stor) fMAX(Q,stor) QMBave QMAXave fMB(Q,stor) fMB(Q,stor) stor_low stor_ave stor_high storage storage Simple Bisection

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