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Reservoir Convergence Algorithms

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

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Reservoir Convergence Algorithms

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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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