A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based on a well posed mathematical formulation and results in a numerical scheme with high flexibility in handling geometrical complexities. This is achieved by means of a three-field approach to split the 1D problems from the bulk 3D problem, and then resorting to the minimization of a properly designed functional to impose matching conditions at the interfaces. Thanks to the structure of the functional, the method allows the use of independent meshes for the various subdomains.

3D-1D coupling on non conforming meshes via a three-field optimization based domain decomposition / Berrone, Stefano; Grappein, Denise; Scialo', Stefano. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 448:(2022), pp. 1-21. [10.1016/j.jcp.2021.110738]

3D-1D coupling on non conforming meshes via a three-field optimization based domain decomposition

Berrone, Stefano;Grappein, Denise;scialo' stefano
2022

Abstract

A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based on a well posed mathematical formulation and results in a numerical scheme with high flexibility in handling geometrical complexities. This is achieved by means of a three-field approach to split the 1D problems from the bulk 3D problem, and then resorting to the minimization of a properly designed functional to impose matching conditions at the interfaces. Thanks to the structure of the functional, the method allows the use of independent meshes for the various subdomains.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2927914