Evolution of vortex-surface fields in viscous Taylor-Green and Kida-Pelz flows

In order to investigate continuous vortex dynamics based on a Lagrangian-like formulation, we develop a theoretical framework and a numerical method for computation of the evolution of a vortex-surface field (VSF) in viscous incompressible flows with simple topology and geometry. Equations describing the continuous, timewise evolution of a VSF from an existing VSF at an initial time are first reviewed. Non-uniqueness in this formulation is resolved by the introduction of a pseudo-time and a corresponding pseudo-evolution in which the evolved field is ‘advected’ by frozen vorticity onto a VSF. A weighted essentially non-oscillatory (WENO) method is used to solve the pseudo-evolution equations in pseudo-time, providing a dissipative-like regularization. Vortex surfaces are then extracted as iso-surfaces of the VSFs at different real physical times. The method is applied to two viscous flows with Taylor–Green and Kida–Pelz initial conditions respectively. Results show the collapse of vortex surfaces, vortex reconnection, the formation and roll-up of vortex tubes, vorticity intensification between anti-parallel vortex tubes, and vortex stretching and twisting. A possible scenario for understanding the transition from a smooth laminar flow to turbulent flow in terms of topology of vortex surfaces is discussed

Effets des approximations numériques et de la modélisation de la turbulence sur la dynamique fine échelle d'un tourbillon de Taylor-Green

L'étude proposée est une étape préliminaire pour le développement d'un solveur hybride RANS/LES pour les écoulements compressibles turbulents basé sur des schémas de haute précision et des modèles de sous-maille avancés. Un tourbillon de Taylor-Green est simulé pour plusieurs choix du nombre de Reynolds en utilisant des schémas centrés d'ordre élevé et différents modèles de sous-maille. Des modèles de type Smagorinsky multi-échelles et dynamique sont comparés au modèle classique et à des modèles de type DES. Pour chaque calcul, on étudie l'effet du maillage et de la discrétisation temporelle

A short note on a 3D spectral analysis for turbulent flows on unstructured meshes

We propose two techniques for computing the energy spectra for 3D unstructured meshes that are consistent across different element types. These techniques can be particularly useful when assessing the dissipation characteristics and the suitability of several popular non-linear high-order methods for implicit large-eddy simulations (iLES). Numerical experiments demonstrate the performance of several element types for iLES of the Taylor-Green vortex, where a significantly different dissipation and dispersion mechanism for each element type is revealed. The energy spectra results are dependent on the technique selected for obtaining them, therefore an additional established technique from the literature is also included for comparison to further analyse their similarities and their differences. These techniques can be an integral tool for the tuning and calibration of non-linear high-order methods that can benefit both explicit and implicit large-eddy simulations (LES)

An Arbitrary Lagrangian-Eulerian SPH-MLS Method for the Computation of Compressible Viscous Flows

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] In this work we present a high-accurate discretization to solve the compressible Navier-Stokes equations using an Arbitrary Lagrangian-Eulerian meshless method (SPH-MLS), which can be seen as a general formulation that includes some well-known meshfree methods as a particular case. The formulation is based on the use of Moving Least Squares (MLS) approximants as weight functions on a Galerkin formulation and to accurate discretize the convective and viscous fluxes. This formulation also verifies the discrete partition of unity and reproduces the zero-gradient condition for constant functions. Convective fluxes are discretized using Riemann solvers. In order to obtain high accuracy MLS is also used for the high-order reconstruction of the Riemann states. The accuracy and performance of the proposed method is demonstrated by solving different steady and unsteady benchmark problems.This work has been partially supported by Ministerio de Ciencia, Innovación y Universidades of the Spanish Government (grant #RTI2018-093366-B-I00) and by the Consellería de Educación e Ordenación Universitaria of the Xunta de Galicia (grant# ED431C 2018/41), cofinanced with FEDER funds of the European Union. Luis Ramírez also acknowledges the funding provided by the Xunta de Galicia through the program Axudas para a mellora, creación, recoñecemento e estruturación de agrupacións estratéxicas do Sistema universitario de Galicia (reference # ED431E 2018/11)Xunta de Galicia; ED431C 2018/41Xunta de Galicia; ED431E 2018/1