Reservoir Convergence Algorithms Convergence Algorithm Previously Used Current Convergence Algorithm

General 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

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

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) These functions started out using this simple convergence algorithm. The first step in an iteration is to calculate the outflow based on the storage of the previous iteration, using the max outflow function. Using that outflow, a storage is determined using the mass balance function. Again, the max outflow function determines an outflow based on this storage value. When these values for outflow converge, the method is exited. This becomes problematic when an area of zero slope is present in one of the curves. Convergence can never be obtained under this scenario using this algorithm. fMB(stor,Q) fMB(stor,Q) storage storage Ideal Problematic

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 To fix that problem an algorithm based on the bisection method was implemented. This is an incremental search method that divides the search interval in half at each iteration 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

2. Bisection Replaces Simple Algorithm The simple algorithm was replaced with the bisection algorithm. This approach also proved to be problematic. outflow outflow fMAX(Q,stor) 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

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