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arXiv2026

Sliding contact fraction in gravity-driven dense cohesionless granular flows

Using large-scale, three-dimensional discrete element simulations, we investigate the kinematic properties of granular chute flows of cohesionless grains, together with the evolution of the coordination number and the fraction of sliding contacts. Our results reveal that, under certain conditions, increasing the grain--grain friction coefficient leads to a decrease in the global dissipation of the system. This finding highlights that the overall dissipation is not solely governed by the energy lost during sliding contacts, but also by the probability that such contacts occur, a probability that decreases markedly as the friction coefficient increases. Together, these effects demonstrate the subtle and nontrivial interplay between grain-scale frictional interactions and macroscopic flow behavior in dense and cohesionless granular materials.

physics.class-ph↗

arXiv2026

Aliasing and phase shifting in pseudo-spectral simulations of the incompressible Navier-Stokes equations

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.

physics.flu-dyn↗