International Journal for Numerical Methods in Fluids

This article provides an overview of the structure of anisotropy in group velocity error when solving the Euler equations using finite difference methods. Analysis of this structure provides understanding to the propagation of error in such solutions and the development of future multidimensionally optimized schemes .

This paper contains a comparison of four SIMPLE-type methods used as solver and as preconditioner for the iterative solution of the (Reynolds-averaged) Navier-Stokes equations. We find SIMPLER preconditioning to be robust and efficient for academic and industrial test cases. The flow around a ship hull at Reynolds number 2E9, for example, on a grid with cell aspect ratio up to 1:1E6, can be computed in 3 instead of 15 h.

The imbalance introduced by a bed or bottom discontinuity is eradicated from the smoothed particle hydrodynamics calculation of the water depth by means of a corrected mass. The imbalance in the source terms in the momentum equation is also removed by using this corrected mass within the bed gradients. The numerical scheme has been tested against a set of analytical and experimental test cases (including dam breaks over steps) showing that the numerical scheme is able to reproduce reference solutions with improved accuracy.

We propose a finite volume scheme to compute the solution of the convection-diffusion equation. The diffusive fluxes are approximated using a recent cell-centred scheme, working on unstructured and possibly non-conforming grids. As in the MUSCL method, the numerical convective fluxes are built with a prediction-limitation process, which ensures that the discrete maximum principle is satisfied; the limitation does not involve any geometrical reconstruction, thus allowing the use of completely general grids, in any space dimension.

We present a robust method to generate hybrid grid for viscous flow analysis (in 2D or 3D), which consists of adaptive Cartesian grid in the background, body-fitted layer near the object, and transition layer connecting the two. The proposed method has been tested with various models including complex geometry and multi-body cases, showing robust results in reasonable computation time.

The present study gathers a deep analysis of the sampling rate reduction and interpolation processes and issues taking place within aeroacoustics hybrid methods. It also provides an original explicit formalism, which allows predicting when and how the aliasing and spuriousing phenomena will occur, whenever a given signal will have to be submitted to sampling and/or interpolation processes.

Appropriate determination of the bin size used for sampling continuum-based properties in small systems consisting of countable particles is considered as a critical issue. In this study, we examine the effective parameters on the sampling of mean flow velocity in molecular dynamics simulations. Then, on the basis of the findings, we propose an optimal range of the bin size that retains the statistical and spatial accuracy of the sampled mean velocity throughout the flow field.