A robust matrix-free approach for large-scale non-isothermal high-contrast viscosity Stokes flow on blended domains with applications to geophysics
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908393618276352 |
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| author | Burkhart, Andreas Kohl, Nils Wohlmuth, Barbara Zawallich, Jan |
| author_facet | Burkhart, Andreas Kohl, Nils Wohlmuth, Barbara Zawallich, Jan |
| contents | We consider a compressible Stokes problem in the quasi-stationary case coupled with a time dependent advection-diffusion equation with special emphasis on high viscosity contrast geophysical mantle convection applications. In space, we use a P2-P1 Taylor--Hood element which is generated by a blending approach to account for the non-planar domain boundary without compromising the stencil data structure of uniformly refined elements. In time, we apply an operator splitting approach for the temperature equation combining the BDF2 method for diffusion and a particle method for advection, resulting in an overall second order scheme. Within each time step, a stationary Stokes problem with a high viscosity contrast has to be solved for which we propose a matrix-free, robust and scalable iterative solver based on Uzawa type block preconditioners, polynomial Chebyshev smoothers and a BFBT type Schur complement approximation. Our implementation is using a hybrid hierarchical grid approach allowing for massively parallel, high resolution Earth convection simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A robust matrix-free approach for large-scale non-isothermal high-contrast viscosity Stokes flow on blended domains with applications to geophysics Burkhart, Andreas Kohl, Nils Wohlmuth, Barbara Zawallich, Jan Numerical Analysis 65N30, 65N55, 65Y05, 65F10, 65Z05 We consider a compressible Stokes problem in the quasi-stationary case coupled with a time dependent advection-diffusion equation with special emphasis on high viscosity contrast geophysical mantle convection applications. In space, we use a P2-P1 Taylor--Hood element which is generated by a blending approach to account for the non-planar domain boundary without compromising the stencil data structure of uniformly refined elements. In time, we apply an operator splitting approach for the temperature equation combining the BDF2 method for diffusion and a particle method for advection, resulting in an overall second order scheme. Within each time step, a stationary Stokes problem with a high viscosity contrast has to be solved for which we propose a matrix-free, robust and scalable iterative solver based on Uzawa type block preconditioners, polynomial Chebyshev smoothers and a BFBT type Schur complement approximation. Our implementation is using a hybrid hierarchical grid approach allowing for massively parallel, high resolution Earth convection simulations. |
| title | A robust matrix-free approach for large-scale non-isothermal high-contrast viscosity Stokes flow on blended domains with applications to geophysics |
| topic | Numerical Analysis 65N30, 65N55, 65Y05, 65F10, 65Z05 |
| url | https://arxiv.org/abs/2506.04157 |