Numerical investigations of the compressible Navier-Stokes system

In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations: a staggered scheme based on the Rusanov one for the inviscid (Euler) system,a staggered pseudo-Lagrangian scheme in which the mesh “follows” the fluid,the Eulerian projection (on a fixed mesh) of the preceding scheme. All these schemes only involve the resolution of linear systems (all the nonlinear terms are solved in an explicit way). We propose numerical illustrations of their behaviors on particular solutions in which the density has discontinuities (hereafter called Hoff solutions). We show that the three schemes seem to converge to the same solutions, and we compare the evolution of the amplitude of the discontinuity of the numerical solution (with the pseudo-Lagrangian scheme) with the one predicted by Hoff and observe a good agreement.

A second-order accurate non-intrusive staggered scheme for the interaction of ultra-lightweight rigid bodies with fluid flow

This paper presents a staggered scheme with second-order temporal accuracy for fluid-structure interaction problems involving ultra-lightweight rigid bodies. The staggered scheme is based on the Dirichlet-Neumann coupling and is non-intrusive. First, the spectral properties of the staggered scheme are studied and also compared against the monolithic scheme using a linear model problem. Later, the suitability and effectiveness of the staggered scheme for problems involving incompressible flows and lightweight rigid solids are illustrated by using the examples of galloping of a square cylinder and lock-in of a circular cylinder for mass-ratio values as low as 0.01. This is the first time in the literature flow-induced vibrations of rigid bodies with such low mass ratio values are successfully simulated using a staggered scheme. Two different fluid solvers are considered to illustrate the non-intrusive nature of the proposed scheme. Guidelines for choosing the relaxation parameter are also provided. With its iteration-free nature and with a single (relaxation) parameter, the proposed staggered scheme renders itself as an accurate and computationally efficient scheme for fluid-rigid body interaction problems, including those involving lightweight structures.