Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq Model
This paper compares two strategies to compute buoyancy-driven flows using stabilized methods. Both formulations are based on a unified approach for solving compressible and incompressible flows, which solves the continuity, momentum, and total energy equations in a coupled entropy-consistent way. Th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/15/8/278 |
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| author | Guillermo Hauke Jorge Lanzarote |
| author_facet | Guillermo Hauke Jorge Lanzarote |
| author_sort | Guillermo Hauke |
| collection | DOAJ |
| description | This paper compares two strategies to compute buoyancy-driven flows using stabilized methods. Both formulations are based on a unified approach for solving compressible and incompressible flows, which solves the continuity, momentum, and total energy equations in a coupled entropy-consistent way. The first approach introduces the variable density thermodynamics of the liquid or gas without any artificial buoyancy terms, i.e., without applying any approximate models into the Navier–Stokes equations. Furthermore, this formulation holds for flows driven by high temperature differences. Further advantages of this formulation are seen in the fact that it conserves the total energy and it lacks the incompressibility inconsistencies due to volume changes induced by temperature variations. The second strategy uses the Boussinesq approximation to account for temperature-driven forces. This method models the thermal terms in the momentum equation through a temperature-dependent nonlinear source term. Computer examples show that the thermodynamic approach, which does not introduce any artificial terms into the Navier–Stokes equations, is conceptually simpler and, with the incompressible stabilization matrix, attains similar residual convergence with iteration count to methods based on the Boussinesq approximation. For the Boussinesq model, the SUPG and SGS methods are compared, displaying very similar computational behavior. Finally, the VMS a posteriori error estimator is applied to adapt the mesh, helping to achieve better accuracy for the same number of degrees of freedom. |
| first_indexed | 2024-03-09T04:49:07Z |
| format | Article |
| id | doaj.art-b2020c0087204d4d8178ee387d985212 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-09T04:49:07Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-b2020c0087204d4d8178ee387d9852122023-12-03T13:12:24ZengMDPI AGAlgorithms1999-48932022-08-0115827810.3390/a15080278Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq ModelGuillermo Hauke0Jorge Lanzarote1Instituto de Ingeniería de Aragón—Universidad de Zaragoza, Area de Mecánica de Fluidos, Escuela de Ingeniería y Arquitectura, C/María de Luna 3, 50018 Zaragoza, SpainRepsol, DE Química, C/Mendez Alvaro, 44, 28045 Madrid, SpainThis paper compares two strategies to compute buoyancy-driven flows using stabilized methods. Both formulations are based on a unified approach for solving compressible and incompressible flows, which solves the continuity, momentum, and total energy equations in a coupled entropy-consistent way. The first approach introduces the variable density thermodynamics of the liquid or gas without any artificial buoyancy terms, i.e., without applying any approximate models into the Navier–Stokes equations. Furthermore, this formulation holds for flows driven by high temperature differences. Further advantages of this formulation are seen in the fact that it conserves the total energy and it lacks the incompressibility inconsistencies due to volume changes induced by temperature variations. The second strategy uses the Boussinesq approximation to account for temperature-driven forces. This method models the thermal terms in the momentum equation through a temperature-dependent nonlinear source term. Computer examples show that the thermodynamic approach, which does not introduce any artificial terms into the Navier–Stokes equations, is conceptually simpler and, with the incompressible stabilization matrix, attains similar residual convergence with iteration count to methods based on the Boussinesq approximation. For the Boussinesq model, the SUPG and SGS methods are compared, displaying very similar computational behavior. Finally, the VMS a posteriori error estimator is applied to adapt the mesh, helping to achieve better accuracy for the same number of degrees of freedom.https://www.mdpi.com/1999-4893/15/8/278buoyant flowsBoussinesq approximationstabilized methodSUPGSGScompressible/ incompressible formulation |
| spellingShingle | Guillermo Hauke Jorge Lanzarote Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq Model Algorithms buoyant flows Boussinesq approximation stabilized method SUPG SGS compressible/ incompressible formulation |
| title | Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq Model |
| title_full | Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq Model |
| title_fullStr | Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq Model |
| title_full_unstemmed | Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq Model |
| title_short | Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq Model |
| title_sort | simulation of low speed buoyant flows with a stabilized compressible incompressible formulation the full navier stokes approach versus the boussinesq model |
| topic | buoyant flows Boussinesq approximation stabilized method SUPG SGS compressible/ incompressible formulation |
| url | https://www.mdpi.com/1999-4893/15/8/278 |
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