Three-dimensional discontinuous Galerkin based high-order gas-kinetic scheme and GPU implementation
In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution p...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wang, Yuhang [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
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| Schlagwörter: |
Graphics processing unit (GPU) |
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| Übergeordnetes Werk: |
Enthalten in: Dissecting the role of Alzheimer's disease susceptibility loci in primary human monocytes: A complex interplay between TREM1, TREM2 and CD33 - Chan, Gail ELSEVIER, 2014, an international journal, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:242 ; year:2022 ; day:30 ; month:06 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.compfluid.2022.105510 |
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| Katalog-ID: |
ELV057980055 |
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| 520 | |a In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. | ||
| 520 | |a In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. | ||
| 650 | 7 | |a Graphics processing unit (GPU) |2 Elsevier | |
| 650 | 7 | |a Discontinuous Galerkin (DG) method |2 Elsevier | |
| 650 | 7 | |a High-order gas-kinetic scheme (HGKS) |2 Elsevier | |
| 700 | 1 | |a Pan, Liang |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier Science |a Chan, Gail ELSEVIER |t Dissecting the role of Alzheimer's disease susceptibility loci in primary human monocytes: A complex interplay between TREM1, TREM2 and CD33 |d 2014 |d an international journal |g Amsterdam [u.a.] |w (DE-627)ELV017359333 |
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10.1016/j.compfluid.2022.105510 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001797.pica (DE-627)ELV057980055 (ELSEVIER)S0045-7930(22)00147-5 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 43.13 bkl 50.17 bkl 58.53 bkl Wang, Yuhang verfasserin aut Three-dimensional discontinuous Galerkin based high-order gas-kinetic scheme and GPU implementation 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. Graphics processing unit (GPU) Elsevier Discontinuous Galerkin (DG) method Elsevier High-order gas-kinetic scheme (HGKS) Elsevier Pan, Liang oth Enthalten in Elsevier Science Chan, Gail ELSEVIER Dissecting the role of Alzheimer's disease susceptibility loci in primary human monocytes: A complex interplay between TREM1, TREM2 and CD33 2014 an international journal Amsterdam [u.a.] (DE-627)ELV017359333 volume:242 year:2022 day:30 month:06 pages:0 https://doi.org/10.1016/j.compfluid.2022.105510 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-GGO GBV_ILN_11 GBV_ILN_23 GBV_ILN_24 GBV_ILN_62 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2015 GBV_ILN_2027 43.13 Umwelttoxikologie VZ 50.17 Sicherheitstechnik VZ 58.53 Abfallwirtschaft VZ AR 242 2022 30 0630 0 |
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10.1016/j.compfluid.2022.105510 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001797.pica (DE-627)ELV057980055 (ELSEVIER)S0045-7930(22)00147-5 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 43.13 bkl 50.17 bkl 58.53 bkl Wang, Yuhang verfasserin aut Three-dimensional discontinuous Galerkin based high-order gas-kinetic scheme and GPU implementation 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. Graphics processing unit (GPU) Elsevier Discontinuous Galerkin (DG) method Elsevier High-order gas-kinetic scheme (HGKS) Elsevier Pan, Liang oth Enthalten in Elsevier Science Chan, Gail ELSEVIER Dissecting the role of Alzheimer's disease susceptibility loci in primary human monocytes: A complex interplay between TREM1, TREM2 and CD33 2014 an international journal Amsterdam [u.a.] (DE-627)ELV017359333 volume:242 year:2022 day:30 month:06 pages:0 https://doi.org/10.1016/j.compfluid.2022.105510 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-GGO GBV_ILN_11 GBV_ILN_23 GBV_ILN_24 GBV_ILN_62 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2015 GBV_ILN_2027 43.13 Umwelttoxikologie VZ 50.17 Sicherheitstechnik VZ 58.53 Abfallwirtschaft VZ AR 242 2022 30 0630 0 |
| allfields_unstemmed |
10.1016/j.compfluid.2022.105510 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001797.pica (DE-627)ELV057980055 (ELSEVIER)S0045-7930(22)00147-5 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 43.13 bkl 50.17 bkl 58.53 bkl Wang, Yuhang verfasserin aut Three-dimensional discontinuous Galerkin based high-order gas-kinetic scheme and GPU implementation 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. Graphics processing unit (GPU) Elsevier Discontinuous Galerkin (DG) method Elsevier High-order gas-kinetic scheme (HGKS) Elsevier Pan, Liang oth Enthalten in Elsevier Science Chan, Gail ELSEVIER Dissecting the role of Alzheimer's disease susceptibility loci in primary human monocytes: A complex interplay between TREM1, TREM2 and CD33 2014 an international journal Amsterdam [u.a.] (DE-627)ELV017359333 volume:242 year:2022 day:30 month:06 pages:0 https://doi.org/10.1016/j.compfluid.2022.105510 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-GGO GBV_ILN_11 GBV_ILN_23 GBV_ILN_24 GBV_ILN_62 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2015 GBV_ILN_2027 43.13 Umwelttoxikologie VZ 50.17 Sicherheitstechnik VZ 58.53 Abfallwirtschaft VZ AR 242 2022 30 0630 0 |
| allfieldsGer |
10.1016/j.compfluid.2022.105510 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001797.pica (DE-627)ELV057980055 (ELSEVIER)S0045-7930(22)00147-5 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 43.13 bkl 50.17 bkl 58.53 bkl Wang, Yuhang verfasserin aut Three-dimensional discontinuous Galerkin based high-order gas-kinetic scheme and GPU implementation 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. Graphics processing unit (GPU) Elsevier Discontinuous Galerkin (DG) method Elsevier High-order gas-kinetic scheme (HGKS) Elsevier Pan, Liang oth Enthalten in Elsevier Science Chan, Gail ELSEVIER Dissecting the role of Alzheimer's disease susceptibility loci in primary human monocytes: A complex interplay between TREM1, TREM2 and CD33 2014 an international journal Amsterdam [u.a.] (DE-627)ELV017359333 volume:242 year:2022 day:30 month:06 pages:0 https://doi.org/10.1016/j.compfluid.2022.105510 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-GGO GBV_ILN_11 GBV_ILN_23 GBV_ILN_24 GBV_ILN_62 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2015 GBV_ILN_2027 43.13 Umwelttoxikologie VZ 50.17 Sicherheitstechnik VZ 58.53 Abfallwirtschaft VZ AR 242 2022 30 0630 0 |
| allfieldsSound |
10.1016/j.compfluid.2022.105510 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001797.pica (DE-627)ELV057980055 (ELSEVIER)S0045-7930(22)00147-5 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 43.13 bkl 50.17 bkl 58.53 bkl Wang, Yuhang verfasserin aut Three-dimensional discontinuous Galerkin based high-order gas-kinetic scheme and GPU implementation 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. Graphics processing unit (GPU) Elsevier Discontinuous Galerkin (DG) method Elsevier High-order gas-kinetic scheme (HGKS) Elsevier Pan, Liang oth Enthalten in Elsevier Science Chan, Gail ELSEVIER Dissecting the role of Alzheimer's disease susceptibility loci in primary human monocytes: A complex interplay between TREM1, TREM2 and CD33 2014 an international journal Amsterdam [u.a.] (DE-627)ELV017359333 volume:242 year:2022 day:30 month:06 pages:0 https://doi.org/10.1016/j.compfluid.2022.105510 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-GGO GBV_ILN_11 GBV_ILN_23 GBV_ILN_24 GBV_ILN_62 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2015 GBV_ILN_2027 43.13 Umwelttoxikologie VZ 50.17 Sicherheitstechnik VZ 58.53 Abfallwirtschaft VZ AR 242 2022 30 0630 0 |
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In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. |
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In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. |
| abstract_unstemmed |
In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier–Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. |
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Different from the traditional discontinuous Galerkin (DG) methods with Riemann solvers, the current method adopts a kinetic evolution process, which is provided by the integral solution of Bhatnagar–Gross–Krook (BGK) model. In the weak formulation of DG method, a time-dependent evolution function is provided, and both inviscid and viscous fluxes can be calculated uniformly. The temporal accuracy is achieved by the two-stage fourth-order discretization, and the second-order gas-kinetic solver is adopted for the fluxes over the cell interface and the fluxes inside a cell. Numerical examples, including accuracy tests and Taylor–Green vortex problem, are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal convergence and super-convergence are achieved by the current scheme. The comparison between DG-HGKS and high-order gas-kinetic scheme with weighted essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the numerical performances are comparable with the approximate number of degree of freedom. To accelerate the computation, the DG-HGKS is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). The obtained results are also compared with those calculated by the central processing units (CPU) code in terms of the computational efficiency. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Graphics processing unit (GPU)</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Discontinuous Galerkin (DG) method</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">High-order gas-kinetic scheme (HGKS)</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pan, Liang</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier Science</subfield><subfield code="a">Chan, Gail ELSEVIER</subfield><subfield code="t">Dissecting the role of Alzheimer's disease susceptibility loci in primary human monocytes: A complex interplay between TREM1, TREM2 and CD33</subfield><subfield code="d">2014</subfield><subfield code="d">an international journal</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV017359333</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:242</subfield><subfield code="g">year:2022</subfield><subfield code="g">day:30</subfield><subfield code="g">month:06</subfield><subfield code="g">pages:0</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.compfluid.2022.105510</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-GGO</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">43.13</subfield><subfield code="j">Umwelttoxikologie</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">50.17</subfield><subfield code="j">Sicherheitstechnik</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">58.53</subfield><subfield code="j">Abfallwirtschaft</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">242</subfield><subfield code="j">2022</subfield><subfield code="b">30</subfield><subfield code="c">0630</subfield><subfield code="h">0</subfield></datafield></record></collection>
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