MONOLITHIC APPROACH FOR SOLVING STOKES-DARCY SYSTEMS
MONOLITHIC APPROACH FOR SOLVING STOKES-DARCY SYSTEMS
PID (if applicable): arxiv:2108.13229
Problem Statement
Instationary, coupled Stokes-Darcy two-domain problem: coupled systems of free flow adjacent to permeable (porous) media
Object of Research and Objective
The motivation for this is to avoid problems when using simple direct solvers (sparse direct solvers for the (linearized) subproblems): bad parallel scaling, untrustworthy solution with bad conditioning.
Procedure
Assemble and solve the above system via block-preconditioning (implemented entirely in DuMux)
File:Https://i.imgur.com/3K2chRh.jpg
Involved Disciplines
Environmental Systems, Mathematics
Data Streams
Model
Stokes flow in the free-flow domain Darcy’s law for the porous domain
Discretization
- Time: first-order backward Euler scheme
- Space: finite volumes
- Porous Domain (Darcy): mit two-point flux approximation for pressure
- Free Flow domain (Stokes): staggered grid for pressure and velocity, upwind scheme for approximation of fluxes
Variables
Name | Unit | Symbol |
---|---|---|
Pressure (Dirichlet pressure) | - | |
Velocity (Neumann velocity) | - |
Process Informationen
Process Steps
Name | Description | Input | Output | Method | Parameter | Environment | Mathematical Area |
---|---|---|---|---|---|---|---|
Solving | Solving with Preconditioner+Solver | LGS | Vector | Solver: PD-GMRES, Preconditioner: AMG, Uzawa, ILU(0), Block-Jacobi, Block-Gauss-Seidel | DuMux | Numerical Mathematics |
Applied Methods
ID | Name | Process Step | Parameter | implemented by |
---|---|---|---|---|
wikidata:Q1069090 | block-Gauss-Seidel preconditioner | Preconditioning | ||
wikidata:Q1481893 | Block Jacobi Preconditioner | Preconditioning | ||
- | Two-domain block-Gauss-Seidel preconditioner | Two-Domain Preconditioning | ||
- | Two-domain Block Jacobi Preconditioner | Two-Domain Preconditioning | ||
wikidata:Q2467290 | Umfpack | Solver | ||
wikidata: Q56564057 | PD-GMRES | Solver | k (subiteration parameter, determined automatically), tolerance: relative residual... | |
wikidata:Q56560244 | Bi-CGSTAB | Solver | tolerance: relative residual... | |
wikidata:Q1471828 | AMG method | Preconditioner | ||
wikidata: Q17144437 | Uzawa-iterations | Preconditioner | ||
wikidata:Q1654069 | ILU(0) factorization | Preconditioner |
Software used
ID | Name | Description | Version | Programming Language | Dependencies | versioned | published | documented |
---|---|---|---|---|---|---|---|---|
sw:14293 | DuMux | DUNE for Multi-{Phase, Component, Scale, Physics, …} flow and transport in porous media | C++, python-bindings, utility-skripts in python | Linux, DuNE (C++ Framework), cmake (module chains), package-config, compiler, build-essentials, dpg | https://git.iws.uni-stuttgart.de/dumux-repositories/dumux | https://zenodo.org/record/5152939#.YQva944zY2w | https://dumux.org/docs/ | |
sw:18749 | ISTL | Iterative Solver Template Library” (ISTL) which is part of the “Distributed and Unified Numerics Environment” (DUNE). | C++ | Linux, DuNE (C++ Rahmenwerk) | https://gitlab.dune-project.org/core/dune-istl | https://doi.org/10.1007/978-3-540-75755-9_82 | https://www.dune-project.org/modules/dune-istl/ |
Hardware
ID | Name | Processor | Compiler | #Nodes | #Cores |
---|---|---|---|---|---|
AMD EPYC 7551P CPU | 1 | 1 |
Input Data
ID | Name | Size | Data Structure | Format Representation | Format Exchange | binary/text | proprietary | to publish | to archive |
---|---|---|---|---|---|---|---|---|---|
LGS | O() Matrix size | Data structure in DUNE/DuMux | numbers | open | ? | ? |
Output Data
ID | Name | Size | Data Structure | Format Representation | Format Exchange | binary/text | proprietary | to publish | to archive |
---|---|---|---|---|---|---|---|---|---|
Solution Vector | Data Structure in DUNE/DuMux | numbers | open | ? | ? | ||||
Runtime Behavior | Data Structure in DUNE/DuMux | numbers | open | ? | ? | ||||
wikidata:Q18812775 | vtk-image files, from the daten structure | ? | ASCII or binary | open | ? | ? |
Reproducibility
Mathematical Reproducibility
yes, by all parameters
Runtime Reproducibility
yes, for same input samples
Reproducibility of Results
Due to floating point arithmetic, no bitwise reproducibility
Reproducibility on original Hardware
Reproducibility on other Hardware
a) Serial Computation
b) Parallel Computation
Transferability to
a) similar model parameters (other initial and boundary values)
b) other models
Legend
The following abbreviations are used in the document to indicate/resolve IDs:
doi: DOI / https://dx.doi.org/
sw: swMATH / https://swmath.org/software/
wikidata: https://www.wikidata.org/wiki/