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Convergence properties of iteratively coupled surface-subsurface models

Schüller, Valentina LU orcid ; Birken, Philipp LU and Dedner, Andreas (2025) In GEM - International Journal on Geomathematics 16(1).
Abstract

Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial differential equations in a partitioned approach via boundary conditions. Full interaction between the subsolvers is ensured by an iterative coupling procedure. This can be accelerated using relaxation. In this paper, we apply continuous and fully discrete linear analysis techniques to study an idealized, linear, 1D-0D version of a surface-subsurface model. These result in explicit expressions for the convergence factor and an optimal relaxation parameter, depending on material and discretization parameters.... (More)

Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial differential equations in a partitioned approach via boundary conditions. Full interaction between the subsolvers is ensured by an iterative coupling procedure. This can be accelerated using relaxation. In this paper, we apply continuous and fully discrete linear analysis techniques to study an idealized, linear, 1D-0D version of a surface-subsurface model. These result in explicit expressions for the convergence factor and an optimal relaxation parameter, depending on material and discretization parameters. We test our analysis results numerically for fully nonlinear 2D-1D experiments based on existing benchmark problems. The linear analysis can explain fast convergence of iterations observed in practice for different materials and test cases, even though we are not able to capture various nonlinear effects.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Convergence analysis, Coupled problems, Iterative methods, Relaxation, Surface-subsurface modeling
in
GEM - International Journal on Geomathematics
volume
16
issue
1
article number
9
pages
33 pages
publisher
Springer
external identifiers
  • scopus:105003297255
ISSN
1869-2672
DOI
10.1007/s13137-025-00265-4
language
English
LU publication?
yes
additional info
Publisher Copyright: © The Author(s) 2025.
id
473250be-e031-4294-b30e-b73a05e9a7ba
date added to LUP
2025-05-26 08:50:14
date last changed
2025-08-13 11:32:29
@article{473250be-e031-4294-b30e-b73a05e9a7ba,
  abstract     = {{<p>Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial differential equations in a partitioned approach via boundary conditions. Full interaction between the subsolvers is ensured by an iterative coupling procedure. This can be accelerated using relaxation. In this paper, we apply continuous and fully discrete linear analysis techniques to study an idealized, linear, 1D-0D version of a surface-subsurface model. These result in explicit expressions for the convergence factor and an optimal relaxation parameter, depending on material and discretization parameters. We test our analysis results numerically for fully nonlinear 2D-1D experiments based on existing benchmark problems. The linear analysis can explain fast convergence of iterations observed in practice for different materials and test cases, even though we are not able to capture various nonlinear effects.</p>}},
  author       = {{Schüller, Valentina and Birken, Philipp and Dedner, Andreas}},
  issn         = {{1869-2672}},
  keywords     = {{Convergence analysis; Coupled problems; Iterative methods; Relaxation; Surface-subsurface modeling}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{Springer}},
  series       = {{GEM - International Journal on Geomathematics}},
  title        = {{Convergence properties of iteratively coupled surface-subsurface models}},
  url          = {{http://dx.doi.org/10.1007/s13137-025-00265-4}},
  doi          = {{10.1007/s13137-025-00265-4}},
  volume       = {{16}},
  year         = {{2025}},
}