This article presents a time-accurate numerical method using high-order accurate compact finite difference scheme for the incompressible Navier–Stokes equations. The method relies on the artificial compressibility formulation, which endows the governing equations a hyperbolic–parabolic nature. The convective terms are discretized with a third-order upwind compact scheme based on flux-difference...

A novel approach combining a two-fluid free surface solver and an efficient hybrid turbulence modelling technique has been presented for the simulation of breaking waves and their interaction with structures. The incompressible Navier-Stokes equations are solved by a cell centred finite volume method based on the artificial compressibility approach. The free surface (water/air interface) is tre...

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second-order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also invest...

HMM-like multiscale integrators and projective integration methods are two different types of multiscale integrators which have been introduced to simulate efficiently systems with widely disparate time scales. The original philosophies of these methods, reviewed here, were quite different. Recently, however, projective integration methods seem to have evolved in a way that make them increasing...

Results are presented for the 3D numerical simulation of the water impact of a wave energy converter in free fall and subsequent heave motion. The solver, AMAZON-3D, employs a Riemann-based finite volume method on a Cartesian cut cell mesh. The computational domain includes both air and water regions with the air/water boundary captured automatically as a discontinuity in the density field ther...

In this paper, the laminar incompressible flow equations are solved by an upwind least-squares meshless method. Due to the difficulties in generating quality meshes, particularly in complex geometries, a meshless method is increasingly used as a new numerical tool. The meshless methods only use clouds of nodes to influence the domain of every node. Thus, they do not require the nodes to be conn...

Several competing artificial compressibility methods for the incompressible flow equations are examined using high-order flux reconstruction method. The established method (ACM) of \citet{Chorin1967} is compared to alternative entropically damped (EDAC) \citet{Clausen2013}, as well an ACM formulation with hyperbolised diffusion. While former requires solution be converged a divergence free stat...

Compressibility factor and viscosity of natural gasses are of great importance in petroleum and chemical engineering. To calculate the natural gas properties in the pipelines, storage systems and reservoirs, the exact values of gas compressibility factor and viscosity are required. A new method that allows accurate determination of compressibility factor and gas viscosity for all types of: swee...

We discuss the thermodynamic signatures for the topological phase transitions into Majorana and Weyl superfluid phases in ultracold Fermi gases in two and three dimensions (2D and 3D) in the presence of Rashba spin-orbit coupling and a Zeeman field. We analyze the thermodynamic properties exhibiting the distinct nature of the topological phase transitions linked with the Majorana fermions (2D F...