A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid Flows
This paper assesses the feasibility of performing topology optimization of laminar incompressible flows governed by the steady-state Navier–Stokes equations using anisotropic mesh adaptation to achieve a high-fidelity description of all fluid–solid interfaces. The present implementation combines an...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-08-01
|
| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/8/8/232 |
| _version_ | 1797584743740473344 |
|---|---|
| author | Wassim Abdel Nour Joseph Jabbour Damien Serret Philippe Meliga Elie Hachem |
| author_facet | Wassim Abdel Nour Joseph Jabbour Damien Serret Philippe Meliga Elie Hachem |
| author_sort | Wassim Abdel Nour |
| collection | DOAJ |
| description | This paper assesses the feasibility of performing topology optimization of laminar incompressible flows governed by the steady-state Navier–Stokes equations using anisotropic mesh adaptation to achieve a high-fidelity description of all fluid–solid interfaces. The present implementation combines an immersed volume method solving stabilized finite element formulations cast in the variational multiscale (VMS) framework and level-set representations of the fluid–solid interfaces, which are used as an a posteriori anisotropic error estimator to minimize interpolation errors under the constraint of a prescribed number of nodes in the mesh. Numerical results obtained for several two-dimensional problems of power dissipation minimization show that the optimal designs are mesh-independent (although the convergence rate does decreases as the number of nodes increases), agree well with reference results from the literature, and provide superior accuracy over prior studies solved on isotropic meshes (fixed or adaptively refined). |
| first_indexed | 2024-03-10T23:56:56Z |
| format | Article |
| id | doaj.art-15fe436550c645208d937ced55dd3357 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T23:56:56Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-15fe436550c645208d937ced55dd33572023-11-19T01:04:48ZengMDPI AGFluids2311-55212023-08-018823210.3390/fluids8080232A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid FlowsWassim Abdel Nour0Joseph Jabbour1Damien Serret2Philippe Meliga3Elie Hachem4Mines Paris, PSL University, Centre for Material Forming (CEMEF), UMR CNRS, 06904 Sophia Antipolis, FranceTEMISTh SAS, Technocentre des Florides, 13700 Marignane, FranceTEMISTh SAS, Technocentre des Florides, 13700 Marignane, FranceMines Paris, PSL University, Centre for Material Forming (CEMEF), UMR CNRS, 06904 Sophia Antipolis, FranceMines Paris, PSL University, Centre for Material Forming (CEMEF), UMR CNRS, 06904 Sophia Antipolis, FranceThis paper assesses the feasibility of performing topology optimization of laminar incompressible flows governed by the steady-state Navier–Stokes equations using anisotropic mesh adaptation to achieve a high-fidelity description of all fluid–solid interfaces. The present implementation combines an immersed volume method solving stabilized finite element formulations cast in the variational multiscale (VMS) framework and level-set representations of the fluid–solid interfaces, which are used as an a posteriori anisotropic error estimator to minimize interpolation errors under the constraint of a prescribed number of nodes in the mesh. Numerical results obtained for several two-dimensional problems of power dissipation minimization show that the optimal designs are mesh-independent (although the convergence rate does decreases as the number of nodes increases), agree well with reference results from the literature, and provide superior accuracy over prior studies solved on isotropic meshes (fixed or adaptively refined).https://www.mdpi.com/2311-5521/8/8/232topology optimizationfluid mechanicslevel-set methodanisotropic mesh adaptation |
| spellingShingle | Wassim Abdel Nour Joseph Jabbour Damien Serret Philippe Meliga Elie Hachem A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid Flows Fluids topology optimization fluid mechanics level-set method anisotropic mesh adaptation |
| title | A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid Flows |
| title_full | A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid Flows |
| title_fullStr | A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid Flows |
| title_full_unstemmed | A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid Flows |
| title_short | A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid Flows |
| title_sort | stabilized finite element framework for anisotropic adaptive topology optimization of incompressible fluid flows |
| topic | topology optimization fluid mechanics level-set method anisotropic mesh adaptation |
| url | https://www.mdpi.com/2311-5521/8/8/232 |
| work_keys_str_mv | AT wassimabdelnour astabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT josephjabbour astabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT damienserret astabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT philippemeliga astabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT eliehachem astabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT wassimabdelnour stabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT josephjabbour stabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT damienserret stabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT philippemeliga stabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows AT eliehachem stabilizedfiniteelementframeworkforanisotropicadaptivetopologyoptimizationofincompressiblefluidflows |