Stable method and apparatus for solving S-shaped non-linear functions utilizing modified Newton-Raphson algorithms
US7505882B2 · kind B2 · utility
Assignee
Inventors
Key dates
| Filing date | Mar 15, 2006 |
| Grant date | Mar 17, 2009 |
| Priority date | — |
| Expiry date | Apr 14, 2027 |
Classification
- Technology area (CPC G)Physics
- CPC primaryG06F30/23
- WIPO fieldComputer technology
- WIPO sectorElectrical engineering
Abstract
An apparatus and method are provided for solving a non-linear S-shaped function F=ƒ(S) which is representative of a property S in a physical system, such saturation in a reservoir simulation. A Newton iteration (T) is performed on the function ƒ(S) at Sv to determine a next iterative value Sv+1. It is then determined whether Sv+1 is located on the opposite side of the inflection point Sc from Sv. If Sv+1 is located on the opposite side of the inflection point from Sv, then Sv+1 is set to Sl, a modified new estimate. The modified new estimate, Sl, is preferably set to either the inflection point, Sc, or to an average value between Sv and Sv+1, i.e., Sl=0.5(Sv+Sv+1). The above steps are repeated until Sv+1 is within the predetermined convergence criteria. Also, solution algorithms are described for two-phase and three-phase flow with gravity and capillary pressure.
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.