Stabilized discretizations for fluid flows and coupled poromechanics
Abstract/Contents
- Abstract
- In this thesis we develop various stabilized spatial discretizations for fluid flow problems and coupled poromechanics. We start by considering isogeometric collocation methods, which have arisen as an efficient alternative to Galerkin discretizations for high-order simulations of mechanics. We wish to apply theses schemes to incompressible flow problems, which requires the development of appropriate stabilization strategies. The classical SUPG method is extended to a collocation setting, which stabilizes spline collocation schemes in highly advective regimes. Simultaneously, we show that PSPG stabilization allows one to collocation mixed problems with an equal-order scheme. We show that these stabilizations are effective are removing instabilities while also retaining the inherent high-order accuracy of spline collocation methods when applied to the scalar advection, incompressible Stokes, and incompressible Navier-Stokes equations. Continuing the focus on isogeometric collocation methods, we move on to consider applications in compressible flows. Stabilization strategies are again needed, in this case so that the scheme can handle shocks. We extend a residual-based, artificial viscosity method for this purpose, and we develop a projection-inspired alternative to SUPG stabilization. Results on a variety of conservation laws show the robustness of the stabilized scheme, again without sacrificing accuracy on smooth problems. We then turn away from isogeometric collocation methods and pure fluid flow problems. The latter half of the thesis considers coupled poromechanics, or the coupled problem of flow through a deformable porous media. We consider spatial discretization using a coupled finite element - finite volume approach using piecewise linear and piecewise constant representations for mechanics and flow, respectively. While commonly used in practice, this discretization choice will exhibit pressure instabilities as undrained conditions are approached due to a lack of inf-sup stability. We show that pressure jump stabilization is effective at removing spurious pressure oscillations that appear in the nearly undrained burden regions when simulating CO2 sequestration, and study numerical properties such as the proper selection of stabilization constants for different meshes. Finally, we consider the performance of iteratively, or sequentially, coupled schemes for poromechanics when undrained regions are present. We clarify the relationship between fractional step schemes and the inf-sup condition, and in particular note that the fact that sequential schemes do not form or invert the full saddle-point matrix at any point is not enough to conclude that spurious pressure oscillations will not appear. However, pressure jump stabilization can be trivially extended to the fixed-stress method considered, and this both removes spurious pressure oscillations and improves the efficiency of the scheme.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2024; ©2024 |
| Publication date | 2024; 2024 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Aronson, Ryan Michael |
|---|---|
| Degree supervisor | Tchelepi, Hamdi |
| Thesis advisor | Tchelepi, Hamdi |
| Thesis advisor | Dunham, Eric |
| Thesis advisor | Evans, John A, (Professor of computational mechanics) |
| Degree committee member | Dunham, Eric |
| Degree committee member | Evans, John A, (Professor of computational mechanics) |
| Associated with | Stanford University, School of Engineering |
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Ryan Michael Aronson. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2024. |
| Location | https://purl.stanford.edu/wn737ys8898 |
Access conditions
- Copyright
- © 2024 by Ryan Michael Aronson
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