In the present work, the Roe, the Steger and Warming, the Van Leer, the Harten, the Frink, Parikh and Pirzadeh, the Liou and Steffen Jr. and the Radespiel and Kroll schemes are implemented, on a finite volume context and using an upwind and unstructured spatial discretization, to solve the Euler equations in the three-dimensional space. The Roe, the Harten, and the Frink, Parikh and Pirzadeh sc...

We propose and analyze spectral direction splitting schemes for the incompressible Navier-Stokes equations. The schemes combine a Legendre-spectral method for the spatial discretization and a pressure-stabilization/direction splitting scheme for the temporal discretization, leading to a sequence of one-dimensional elliptic equations at each time step while preserving the same order of accuracy ...

The investigation of exponentially small splitting of separatrices for high-frequency time-periodic perturbation of a Hamiltonian with one degree of freedom leads to a reference system in the complex phase space. The reference system is independent of a small parameter, e.g., the perturbation period of the original system. The splitting of the invariant manifolds is described for the system v 2...

Among the various approaches for parallel depthrst search (DFS), the stack-splitting schemes are most popular. However, as shown in this paper, dynamical stack-splitting is not suitable for massively parallel systems with several hundred processors. Initial work-load imbalances and work packets of dissimilar sizes cause a high communication overhead. We compare work-load balancing strategies of...

The lattice Boltzmann space/time discretisation, as usually derived from integration along characteristics, is shown to correspond to a Strang splitting between decoupled streaming and collision steps. Strang splitting offers a second-order accurate approximation to evolution under the combination of two non-commuting operators, here identified with the streaming and collision terms in the disc...

We discover a fundamental mechanism for the sharp increase in the diffusion rate of the motion of a charged particle in a uniform magnetic field when a time-periodic electricfield propagating orthogonally to the magnetic field is slightly tilted. It is associated with the degeneracies of the underlying motion; in fact, a two-degree of freedom mechanism of instability induces this behaviour. Unf...

Abstract Photocatalytic water splitting system using particulate semiconductor materials is a promising strategy for converting solar energy into hydrogen and oxygen. In particular, visible-light-driven ‘Z-scheme’ printable photocatalyst sheets are cost-effective scalable. However, little known about the fundamental photophysical processes, which key to explaining promoting photoactivity. Here,...