Use of algebraic dual spaces in domain decomposition methods for Darcy flow in 3D domains

Jain, V.; Palha da Silva Clérigo, A.; Gerritsma, M.I.

doi:10.1016/j.cma.2022.115827

Use of algebraic dual spaces in domain decomposition methods for Darcy flow in 3D domains

Title

Use of algebraic dual spaces in domain decomposition methods for Darcy flow in 3D domains

Author

Jain, V. (TU Delft Aerodynamics)
Palha da Silva Clérigo, A. (TU Delft Aerodynamics)
Gerritsma, M.I. (TU Delft Aerodynamics)

Date

2023

Abstract

In this work we use algebraic dual spaces with a domain decomposition method to solve the Darcy equations. We define the broken Sobolev spaces and their finite dimensional counterparts. A global trace space is defined that connects the solution between the broken spaces. Use of algebraic dual spaces results in a sparse, metric-free representation of the incompressibility constraint, the pressure gradient term, and on the continuity constraint between the sub domains. To demonstrate this, we solve two test cases: (i) a manufactured solution case, and (ii) an industrial benchmark reservoir modelling problem SPE10. The results demonstrate that the dual spaces can be used for domain decomposition formulation, and despite having more unknowns, requires less simulation time compared to the continuous Galerkin formulation, without compromising on the accuracy of the solution.

Subject

Algebraic dual spaces
Darcy equations
Domain decomposition
Hybrid finite elements
Mimetic spectral element method
SPE10

To reference this document use:

http://resolver.tudelft.nl/uuid:dc3952be-47af-4ccd-99a8-dc6188df000d

DOI

https://doi.org/10.1016/j.cma.2022.115827

ISSN

0045-7825

Source

Computer Methods in Applied Mechanics and Engineering, 404

Part of collection

Institutional Repository