Numerical dissipation induced by the low-pass filtering in nonlinear gyrokinetic simulations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911856873963520 |
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| author | Wang, Zihao Wang, Shaojie |
| author_facet | Wang, Zihao Wang, Shaojie |
| contents | De-aliasing is an essential procedure for eliminating the aliasing error in nonlinear simulations, such as nonlinear gyrokinetic turbulence simulations. An ideal approach to de-aliasing in the periodic dimension is Fourier truncation. Finite difference low-pass filtering applied in the non-periodic direction strongly dampens aliasing modes. At the same time, it induces numerical dissipation in the region of the physically realistic solution. It is shown analytically that the long-wave dissipation coefficient is proportional to the (Np-3) power of the wavenumber under desirable constraints satisfying the highest order accuracy, where Np is the number of filter points. Numerical results after applying the optimised low-pass filtering to the nonlinear gyrokinetic turbulence simulation suggest that the nine-point format preserves intact mesoscopic zonal structures in Tokamak plasmas, and is therefore suitable for long-time nonlinear turbulence simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_18139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical dissipation induced by the low-pass filtering in nonlinear gyrokinetic simulations Wang, Zihao Wang, Shaojie Plasma Physics De-aliasing is an essential procedure for eliminating the aliasing error in nonlinear simulations, such as nonlinear gyrokinetic turbulence simulations. An ideal approach to de-aliasing in the periodic dimension is Fourier truncation. Finite difference low-pass filtering applied in the non-periodic direction strongly dampens aliasing modes. At the same time, it induces numerical dissipation in the region of the physically realistic solution. It is shown analytically that the long-wave dissipation coefficient is proportional to the (Np-3) power of the wavenumber under desirable constraints satisfying the highest order accuracy, where Np is the number of filter points. Numerical results after applying the optimised low-pass filtering to the nonlinear gyrokinetic turbulence simulation suggest that the nine-point format preserves intact mesoscopic zonal structures in Tokamak plasmas, and is therefore suitable for long-time nonlinear turbulence simulations. |
| title | Numerical dissipation induced by the low-pass filtering in nonlinear gyrokinetic simulations |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2404.18139 |