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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.08892 |
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| _version_ | 1866914468819107840 |
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| author | Lambert, Clovis Reneuve, Jason Augier, Pierre |
| author_facet | Lambert, Clovis Reneuve, Jason Augier, Pierre |
| contents | Pseudo-spectral methods are widely used for direct numerical simulations of turbulence, but the standard 2/3 truncation rule for dealiasing is computationally expensive -- accounting for up to 80% of the total cost in three dimensions. Phase shifting methods provide a more efficient alternative by canceling aliasing errors the combination of nonlinear terms evaluated on shifted grids, allowing the same physical resolution to be achieved on a coarser numerical grid. Despite their use in high-resolution turbulence codes, these methods remain poorly documented in the literature and no open-source implementation exists. This paper presents a comprehensive analysis of phase-shifting dealiasing for pseudo-spectral simulations of the incompressible Navier-Stokes equations. We derive the aliasing mechanism from quadratic nonlinearities in discrete Fourier space and explain how phase-shifting cancels aliasing contributions exactly or approximately depending on the time-stepping scheme. We describe and compare several algorithms -- including the exact and approximate RK2 phase-shifting schemes of Patterson Jr and Orszag (1971) and Rogallo (1981), and an extension to forced flows -- and discuss their interaction with different truncation geometries in three dimensions. All algorithms are implemented in the open-source framework Fluidsim, providing the first publicly available implementation of phase-shifting dealiasing for pseudo spectral Navier-Stokes solvers. We evaluate the methods on two test cases: the transition to turbulence of Taylor-Green vortices and forced homogeneous isotropic turbulence at $Re_λ= 200$. Phase-shifting methods achieve speedups of up to a factor of 3 compared to RK4 with 2/3 truncation at the same maximum wavenumber, with small accuracy loss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08892 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Aliasing and phase shifting in pseudo-spectral simulations of the incompressible Navier-Stokes equations Lambert, Clovis Reneuve, Jason Augier, Pierre Fluid Dynamics Computational Physics Pseudo-spectral methods are widely used for direct numerical simulations of turbulence, but the standard 2/3 truncation rule for dealiasing is computationally expensive -- accounting for up to 80% of the total cost in three dimensions. Phase shifting methods provide a more efficient alternative by canceling aliasing errors the combination of nonlinear terms evaluated on shifted grids, allowing the same physical resolution to be achieved on a coarser numerical grid. Despite their use in high-resolution turbulence codes, these methods remain poorly documented in the literature and no open-source implementation exists. This paper presents a comprehensive analysis of phase-shifting dealiasing for pseudo-spectral simulations of the incompressible Navier-Stokes equations. We derive the aliasing mechanism from quadratic nonlinearities in discrete Fourier space and explain how phase-shifting cancels aliasing contributions exactly or approximately depending on the time-stepping scheme. We describe and compare several algorithms -- including the exact and approximate RK2 phase-shifting schemes of Patterson Jr and Orszag (1971) and Rogallo (1981), and an extension to forced flows -- and discuss their interaction with different truncation geometries in three dimensions. All algorithms are implemented in the open-source framework Fluidsim, providing the first publicly available implementation of phase-shifting dealiasing for pseudo spectral Navier-Stokes solvers. We evaluate the methods on two test cases: the transition to turbulence of Taylor-Green vortices and forced homogeneous isotropic turbulence at $Re_λ= 200$. Phase-shifting methods achieve speedups of up to a factor of 3 compared to RK4 with 2/3 truncation at the same maximum wavenumber, with small accuracy loss. |
| title | Aliasing and phase shifting in pseudo-spectral simulations of the incompressible Navier-Stokes equations |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2603.08892 |