Lie-symmetry based integrators are constructed in order to preserve the local invariance properties of the equations. The geometrical methods leading to discretized equations for numericalâ€¦ (More)

In this work, the non-isothermal Navierâ€“Stokes equations are studied from the group theory point of view. The symmetry group of the equations is presented and discussed. Some standard turbulenceâ€¦ (More)

Some of the most important geometric integrators for both ordinary and partial differential equations are reviewed and illustrated with examples in mechanics. The class of Hamiltonian differentialâ€¦ (More)

Invariant numerical schemes possess properties that may overcome the numerical properties of most of classical schemes. When they are constructed with moving frames, invariant schemes can presentâ€¦ (More)

Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, . . . ), symmetries are used to analyse common turbulence models. A classâ€¦ (More)

In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundlesâ€¦ (More)

In this work, we present contributions concerning a mathematical study of the sensitivity of a reduced order model (ROM) by the proper orthogonal decomposition (POD) technique applied to aâ€¦ (More)