Localized Computation of Newton Updates in Fully-implicit Two-phase Flow Simulation
| Autor: | Soham M. Sheth, Rami M. Younis |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematical optimization
Computer simulation Scale (ratio) Computer science Computation Multiphase flow Newton's Method 010103 numerical & computational mathematics 01 natural sciences 010305 fluids & plasmas Reduction (complexity) Nonlinear system symbols.namesake Fully-Implicit Localization 0103 physical sciences Benchmark (computing) symbols General Earth and Planetary Sciences and porous media 0101 mathematics Algorithm Newton's method General Environmental Science |
| Zdroj: | ICCS |
| ISSN: | 1877-0509 |
| DOI: | 10.1016/j.procs.2016.05.445 |
| Popis: | Fully-Implicit (FI) Methods are often employed in the numerical simulation of large-scale subsurface flows in porous media. At each implicit time step, a Newton-like method is used to solve the FI discrete nonlinear algebraic system. The linear solution process for the Newton updates is the computational workhorse of FI simulations. Empirical observations suggest that the computed Newton updates during FI simulations of multiphase flow are often sparse. Moreover, the level of sparsity observed can vary dramatically from iteration to the next, and across time steps. In several large scale applications, it was reported that the level of sparsity in the Newton update can be as large as 99%. This work develops a localization algorithm that conservatively predetermines the sparsity pattern of the Newton update. Subsequently, only the flagged nonzero components of the system need be solved. The localization algorithm is developed for general FI models of two phase flow. Large scale simulation results of benchmark reservoir models show a 10 to 100 fold reduction in computational cost for homogeneous problems, and a 4 to 10 fold reduction for strongly heterogeneous problems. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|