Development of Discontinuous Galerkin Methods and a Parallel Simulator for Reservoir Simulation
Bibliographic record
Abstract
Abstract The classical discontinuous Galerkin (DG) methods are designed for elliptic (parabolic) problems and hyperbolic problems. For reservoir simulations, the pressure equation from the black oil model is elliptic (parabolic), while the equations for saturations are hyperbolic. Due to this special property, it is difficult to directly apply the discontinuous Galerkin methods to the black oil model. In this paper, we extend the discontinuous Galerkin methods to reservoir simulations. In our schemes, the local discontinuous Galerkin (LDG) method is used to discretize the black oil model. The upwind concept is combined with the numerical flux term of the LDG method to simulate the direction of propagation of the multiphase flow in reservoirs to avoid the unphysical solutions. We also extend the Peaceman model to the discontinuous Galerkin methods on unstructured grids. Based on the extended discontinuous Galerkin methods, we employ the iterative implicit pressure-explicit saturation (iterative-IMPES) and fully implicit (FIM) methods to solve the coupled nonlinear black oil model. A parallel simulator is implemented using the parallel adaptive finite element package, Parallel Hierarchical Grid (PHG), and validated by testing the first and ninth SPE Comparative Solution Projects. The parallel scalability of our simulator is also tested by a large scale case.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".