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Convergence Properties of Iteratively Coupled Surface-Subsurface Models

Schüller, Valentina LU orcid ; Birken, Philipp LU and Dedner, Andreas (2024)
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. (Less)
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author
; and
organization
publishing date
type
Working paper/Preprint
publication status
published
subject
publisher
arXiv.org
DOI
10.48550/arXiv.2408.12582
language
English
LU publication?
yes
id
a8b9f439-f8b9-4db5-bba5-7af2351704a7
date added to LUP
2024-08-27 11:36:39
date last changed
2024-10-03 10:45:27
@misc{a8b9f439-f8b9-4db5-bba5-7af2351704a7,
  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.<br/>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.}},
  author       = {{Schüller, Valentina and Birken, Philipp and Dedner, Andreas}},
  language     = {{eng}},
  note         = {{Preprint}},
  publisher    = {{arXiv.org}},
  title        = {{Convergence Properties of Iteratively Coupled Surface-Subsurface Models}},
  url          = {{http://dx.doi.org/10.48550/arXiv.2408.12582}},
  doi          = {{10.48550/arXiv.2408.12582}},
  year         = {{2024}},
}