Response of plane viscous jet to entrance flow rate perturbation

Abstract

SUMMARYA two-dimensional numerical simulation solving unsteady incompressible Navier -Stokes equations is used to study the natural varicose instability of a plane jet in the Reynolds number range of 100 -900. A transient train of vortices is observed at the beginning of the computation. It disappears yielding a steady flow. This flow is then used at the basis for forced excitation in order to study the space time development of instability. A Reynolds number dependant behaviour is observed which implies that viscosity directly affects the vortex dynamics.

Solving density driven flow problems with efficient spatial discretizations and higher-order time integration methods

“…Several papers have been devoted to MPFA methods recently [1,2,19,39] and to the link between MPFA and Raviart Thomas and Brezzi-Douglas-Marini MFE [40,46,65,70,71]. In the following, the main stages for the DG-MPFA spatial discretization are recalled in order to use this formulation within the MOL context.…”

“…Indeed, both are locally conservative and handle general irregular grids on anisotropic heterogeneous domains. The MPFA method is preferred to MFE since it can be combined with the DG method without the time splitting procedure [72]. Indeed, MPFA uses the same type of unknowns (average value per element) than DG and therefore, both discretizations can be gathered into one system matrix.…”

“…The variational formulation of (14) over the element E using / E i as test functions gives (see [72]),…”

“…On the other hand, the MPFA method is locally conservative and handle general irregular grids on anisotropic heterogeneous domains [1,2,19,39,67]. The MPFA method uses the same type of unknowns (average value per element) than the DG method and therefore, both discretizations can be gathered into one system matrix [72]. The spatial discretization (MFE_DG_MPFA) based upon the combination of MFE, DG and MPFA methods was shown to be robust and accurate for modelling density driven flow problems [4].…”

“…Indeed, the mixed finite element (MFE) method is used for the flow equation since it is locally conservative and produces accurate and consistent velocity field even for highly heterogeneous domains [18]. For the transport equation, the discontinuous Galerkin (DG) method is used to discretize the advection equation and combined with the multipoint flux approximation (MPFA) method for the discretization of the dispersion equation [72]. The DG method combines the advantageous of the finite element (FE) and finite volume (FV) methods to obtain a robust and accurate numerical scheme for problems involving sharp fronts [59].…”