In this article, we propose to investigate numerically the steady bifurcation points and
bifurcated branches in fluid mechanics by employing high‐order mesh‐free geometric …

This paper is concerned with a Taylor series–based continuation algorithm, the so‐called
Asymptotic Numerical Method (ANM). It describes a generic continuation procedure to apply …

The literature about the asymptotic numerical method (ANM) is reviewed in this paper as
well as its application to hyperelasticity and elastoplasticity. ANM is a generic continuation …

This paper presents the outcome of power series analysis in the framework of the Asymptotic
Numerical Method. We theoretically demonstrate and numerically evidence that the …

In this paper, we propose for the first time to extend the application field of the high‐order
mesh‐free approach to the stationary incompressible Navier‐Stokes equations. This …

Two original algorithms are proposed for the computation of bifurcation points in fluid
mechanics. These algorithms consist of finding the zero values of a specific indicator. To …

This paper deals with the computation of steady bifurcations in the framework of 2D
incompressible Navier–Stokes flow. We first propose a numerical method to accurately …

We have developed a numerical model to efficiently compute steady-state combined
buoyancy and thermocapillary convection solutions. It features a parallel computer …

This paper deals with the computation of Hopf bifurcation points in fluid mechanics. This
computation is done by coupling a bifurcation indicator proposed recently (Cadou et al …

The present works is focused on studying bifurcating solutions in compressible fluid
dynamics. On one side, the physics of the problem is thoroughly investigated using high …