Finite-Volume Flux Reconstruction and Semi-Analytical Particle Tracking for Finite-Element-Type Models of Variably Saturated Flow in Porous Media
Bibliographic record
Abstract
Particle tracking is the most direct and a computationally efficient method to determine travel times and trajectories in subsurface flow modeling. Accurate and consistent particle tracking requires element-wise mass conservation and conforming velocity fields, which ensure continuity of the normal-flow component on element boundaries. These conditions are not met by standard finite-element-type methods. Despite this shortcoming, finite-element-type methods are often used in subsurface flow modeling because they continuously approximate the potential-head field and can easily handle unstructured grids and full material tensors. Acknowledging these advantages and the wide-spread use of finite-element-type models in subsurface flow simulations, we present a novel postprocessing technique that reconstructs a cell-centered finite-volume approximation from a finite-element-type primal solution of the variably-saturated subsurface flow equation to obtain conforming, mass-conservative fluxes. Using the resulting velocity fields, we derive a semi-analytical, parallelized particle tracking scheme applicable to triangular prisms, which leads to consistent and mass-conservative trajectories and associated travel times. Compared to other postprocessing schemes, our flux reconstruction is stable, robust, and fast as it only solves a linear elliptic problem on the order of the number of elements, whereas the original flow problem was transient and non-linear. The methods are implemented as postprocessing codes and linked to the finite-element-type code HydroGeoSphere, but could also be linked to any other software yielding a solution of variably saturated flow in porous media on triangular prisms. The postprocessing codes can handle catchment-scale models including heterogeneous materials, geometries, and boundary conditions, and facilitate to track a million particles through a catchment in just a few minutes on a Standard-PC in Matlab. The approach is described by Selzer et al. (2021).
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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) | 0.001 | 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".