Explaining the Lack of Mesh Convergence of Inviscid Adjoint Solutions near Solid Walls for Subcritical Flows
Numerical solutions to the adjoint Euler equations have been found to diverge with mesh refinement near walls for a variety of flow conditions and geometry configurations. The issue is reviewed, and an explanation is provided by comparing a numerical incompressible adjoint solution with an analytic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Aerospace |
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| Online Access: | https://www.mdpi.com/2226-4310/10/5/392 |
| _version_ | 1797601633486503936 |
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| author | Carlos Lozano Jorge Ponsin |
| author_facet | Carlos Lozano Jorge Ponsin |
| author_sort | Carlos Lozano |
| collection | DOAJ |
| description | Numerical solutions to the adjoint Euler equations have been found to diverge with mesh refinement near walls for a variety of flow conditions and geometry configurations. The issue is reviewed, and an explanation is provided by comparing a numerical incompressible adjoint solution with an analytic adjoint solution, showing that the anomaly observed in numerical computations is caused by a divergence of the analytic solution at the wall. The singularity causing this divergence is of the same type as the well-known singularity along the incoming stagnation streamline, and both originate at the adjoint singularity at the trailing edge. The argument is extended to cover the fully compressible case, in subcritical flow conditions, by presenting an analytic solution that follows the same structure as the incompressible one. |
| first_indexed | 2024-03-11T04:03:05Z |
| format | Article |
| id | doaj.art-de19aae3a60a402e9ba1f559558ceba5 |
| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-03-11T04:03:05Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-de19aae3a60a402e9ba1f559558ceba52023-11-17T23:59:34ZengMDPI AGAerospace2226-43102023-04-0110539210.3390/aerospace10050392Explaining the Lack of Mesh Convergence of Inviscid Adjoint Solutions near Solid Walls for Subcritical FlowsCarlos Lozano0Jorge Ponsin1Computational Aerodynamics Group, National Institute of Aerospace Technology (INTA), Carretera de Ajalvir, Km 4, 28850 Torrejón de Ardoz, SpainComputational Aerodynamics Group, National Institute of Aerospace Technology (INTA), Carretera de Ajalvir, Km 4, 28850 Torrejón de Ardoz, SpainNumerical solutions to the adjoint Euler equations have been found to diverge with mesh refinement near walls for a variety of flow conditions and geometry configurations. The issue is reviewed, and an explanation is provided by comparing a numerical incompressible adjoint solution with an analytic adjoint solution, showing that the anomaly observed in numerical computations is caused by a divergence of the analytic solution at the wall. The singularity causing this divergence is of the same type as the well-known singularity along the incoming stagnation streamline, and both originate at the adjoint singularity at the trailing edge. The argument is extended to cover the fully compressible case, in subcritical flow conditions, by presenting an analytic solution that follows the same structure as the incompressible one.https://www.mdpi.com/2226-4310/10/5/392adjoint Euler equationsanalytic adjoint solutionwall singularitymesh dependence |
| spellingShingle | Carlos Lozano Jorge Ponsin Explaining the Lack of Mesh Convergence of Inviscid Adjoint Solutions near Solid Walls for Subcritical Flows Aerospace adjoint Euler equations analytic adjoint solution wall singularity mesh dependence |
| title | Explaining the Lack of Mesh Convergence of Inviscid Adjoint Solutions near Solid Walls for Subcritical Flows |
| title_full | Explaining the Lack of Mesh Convergence of Inviscid Adjoint Solutions near Solid Walls for Subcritical Flows |
| title_fullStr | Explaining the Lack of Mesh Convergence of Inviscid Adjoint Solutions near Solid Walls for Subcritical Flows |
| title_full_unstemmed | Explaining the Lack of Mesh Convergence of Inviscid Adjoint Solutions near Solid Walls for Subcritical Flows |
| title_short | Explaining the Lack of Mesh Convergence of Inviscid Adjoint Solutions near Solid Walls for Subcritical Flows |
| title_sort | explaining the lack of mesh convergence of inviscid adjoint solutions near solid walls for subcritical flows |
| topic | adjoint Euler equations analytic adjoint solution wall singularity mesh dependence |
| url | https://www.mdpi.com/2226-4310/10/5/392 |
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