On the Geometric Conservation Law for the Non Linear Frequency Domain and Time-Spectral methods
The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Benoit, Marc [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019transfer abstract |
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| Schlagwörter: |
Geometric Conservation Law (GCL) |
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| Umfang: |
39 |
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| Übergeordnetes Werk: |
Enthalten in: Does enhanced hydration have impact on autogenous deformation of internally cued mortar? - Zou, Dinghua ELSEVIER, 2019, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:355 ; year:2019 ; day:1 ; month:10 ; pages:690-728 ; extent:39 |
| Links: |
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| DOI / URN: |
10.1016/j.cma.2019.04.002 |
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ELV04757562X |
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| 520 | |a The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. | ||
| 520 | |a The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. | ||
| 650 | 7 | |a Geometric Conservation Law (GCL) |2 Elsevier | |
| 650 | 7 | |a Computational fluid dynamics |2 Elsevier | |
| 650 | 7 | |a Non Linear Frequency Domain (NLFD) method |2 Elsevier | |
| 650 | 7 | |a Deforming mesh |2 Elsevier | |
| 650 | 7 | |a Numerical method |2 Elsevier | |
| 650 | 7 | |a Time-Spectral method |2 Elsevier | |
| 700 | 1 | |a Nadarajah, Siva |4 oth | |
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10.1016/j.cma.2019.04.002 doi GBV00000000000717.pica (DE-627)ELV04757562X (ELSEVIER)S0045-7825(19)30199-9 DE-627 ger DE-627 rakwb eng 690 VZ 56.45 bkl Benoit, Marc verfasserin aut On the Geometric Conservation Law for the Non Linear Frequency Domain and Time-Spectral methods 2019transfer abstract 39 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. Geometric Conservation Law (GCL) Elsevier Computational fluid dynamics Elsevier Non Linear Frequency Domain (NLFD) method Elsevier Deforming mesh Elsevier Numerical method Elsevier Time-Spectral method Elsevier Nadarajah, Siva oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:355 year:2019 day:1 month:10 pages:690-728 extent:39 https://doi.org/10.1016/j.cma.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 355 2019 1 1001 690-728 39 |
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10.1016/j.cma.2019.04.002 doi GBV00000000000717.pica (DE-627)ELV04757562X (ELSEVIER)S0045-7825(19)30199-9 DE-627 ger DE-627 rakwb eng 690 VZ 56.45 bkl Benoit, Marc verfasserin aut On the Geometric Conservation Law for the Non Linear Frequency Domain and Time-Spectral methods 2019transfer abstract 39 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. Geometric Conservation Law (GCL) Elsevier Computational fluid dynamics Elsevier Non Linear Frequency Domain (NLFD) method Elsevier Deforming mesh Elsevier Numerical method Elsevier Time-Spectral method Elsevier Nadarajah, Siva oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:355 year:2019 day:1 month:10 pages:690-728 extent:39 https://doi.org/10.1016/j.cma.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 355 2019 1 1001 690-728 39 |
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10.1016/j.cma.2019.04.002 doi GBV00000000000717.pica (DE-627)ELV04757562X (ELSEVIER)S0045-7825(19)30199-9 DE-627 ger DE-627 rakwb eng 690 VZ 56.45 bkl Benoit, Marc verfasserin aut On the Geometric Conservation Law for the Non Linear Frequency Domain and Time-Spectral methods 2019transfer abstract 39 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. Geometric Conservation Law (GCL) Elsevier Computational fluid dynamics Elsevier Non Linear Frequency Domain (NLFD) method Elsevier Deforming mesh Elsevier Numerical method Elsevier Time-Spectral method Elsevier Nadarajah, Siva oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:355 year:2019 day:1 month:10 pages:690-728 extent:39 https://doi.org/10.1016/j.cma.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 355 2019 1 1001 690-728 39 |
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10.1016/j.cma.2019.04.002 doi GBV00000000000717.pica (DE-627)ELV04757562X (ELSEVIER)S0045-7825(19)30199-9 DE-627 ger DE-627 rakwb eng 690 VZ 56.45 bkl Benoit, Marc verfasserin aut On the Geometric Conservation Law for the Non Linear Frequency Domain and Time-Spectral methods 2019transfer abstract 39 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. Geometric Conservation Law (GCL) Elsevier Computational fluid dynamics Elsevier Non Linear Frequency Domain (NLFD) method Elsevier Deforming mesh Elsevier Numerical method Elsevier Time-Spectral method Elsevier Nadarajah, Siva oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:355 year:2019 day:1 month:10 pages:690-728 extent:39 https://doi.org/10.1016/j.cma.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 355 2019 1 1001 690-728 39 |
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10.1016/j.cma.2019.04.002 doi GBV00000000000717.pica (DE-627)ELV04757562X (ELSEVIER)S0045-7825(19)30199-9 DE-627 ger DE-627 rakwb eng 690 VZ 56.45 bkl Benoit, Marc verfasserin aut On the Geometric Conservation Law for the Non Linear Frequency Domain and Time-Spectral methods 2019transfer abstract 39 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. Geometric Conservation Law (GCL) Elsevier Computational fluid dynamics Elsevier Non Linear Frequency Domain (NLFD) method Elsevier Deforming mesh Elsevier Numerical method Elsevier Time-Spectral method Elsevier Nadarajah, Siva oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:355 year:2019 day:1 month:10 pages:690-728 extent:39 https://doi.org/10.1016/j.cma.2019.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 355 2019 1 1001 690-728 39 |
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on the geometric conservation law for the non linear frequency domain and time-spectral methods |
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On the Geometric Conservation Law for the Non Linear Frequency Domain and Time-Spectral methods |
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The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. |
| abstractGer |
The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. |
| abstract_unstemmed |
The aim of this paper is to present and validate two new procedures to enforce the Geometric Conservation Law (GCL) on a moving grid for an Arbitrary Lagrangian Eulerian (ALE) formulation for the Euler equations discretized in time for either the Non Linear Frequency Domain (NLFD) or Time-Spectral (TS) methods. The equations are spatially discretized by a structured finite-volume scheme on a hexahedral mesh. The derived methodologies follow a general approach where the positions and the velocities of the grid points are known at each time step. The integrated face mesh velocities are derived either from the Approximation of the Exact Volumetric Increments (AEVI) relative to the undeformed mesh or exactly computed based on a Trilinear Mapping (TRI-MAP) between the physical space and the computational domain. The accuracy of the AEVI method highly depends on the computation of the volumetric increments and limits the temporal-order of accuracy of the deduced integrated face mesh velocities to between one and two. Thus defeating the purpose of the NLFD method which possesses spectral rate of convergence. However, the TRI-MAP method has proven to be more computationally efficient, ensuring the satisfaction of the GCL once the convergence of the temporal derivative of the cell volume is reached in Fourier space. The methods are validated numerically by verifying the conservation of uniform flow and by comparing the integrated face mesh velocities to the exact values derived from the mapping. Their performances for aerodynamic simulation are evaluated for a pitching NACA0012 airfoil. |
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