Combined spectral-finite difference time discretization for periodic and quasi-periodic flows

AbstractAn accurate and efficient treatment of periodic and quasi-periodic flows based on the temporal Fourier decomposition of the Navier-Stokes equations is suggested. A numerical implementation for a laminar afterbody wake in a two-dimensional channel is presented. This implementation is formulated in primitive variables and uses an ordinary 2nd-order accurate finite volume space discretization combined with a standard pressure correction procedure. A multi-step time marching scheme for numerical and physical transients is developed. For flows with a variable dominant period, a period correction algorithm is used. The transients characterizing the instability development are simulated. The numerical results obtained for the afterbody wake confirm the expectations concerning the efficiency and high time accuracy of the method. Moreover, the method provides direct access to quantities difficult to obtain by other methods such as the envelope and the angular velocity variation of the unstable mode

MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM

This paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified equation to the properties of the considered numerical methods

Numerical simulations of wave breaking

This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments

Déferlement de vague : approche multi-pas

Nous simulons numériquement le déferlement de vagues par un modèle d'écoulement multi fluide à faible Mach grâce à une formulation explicite efficacement parallélisable. Le modèle repose sur un schéma par volumes finis de type Godunov du second ordre en temps et en espace et éventuellement un raidissement de l'interface. Nous introduisons une approche multi-pas qui autorise de conséquents gains en temps de calcul. Cette approche est validée par des confrontations expérience /simulation sur le déferlement de vague solitaire 2D sur plan incliné et la rupture de barrage 3D avec obstacle

Surface current dynamics under sea breeze conditions observed by simultaneous HF radar, ADCP and drifter measurements

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Numerical simulation of three-dimensional lee waves behind an isolated hill

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Secondary flows induced by wind forcing in the Rhône region of freshwater influence

Secondary flows induced by the blocking effect of a river plume on a transverse upwelling are investigated in a microtidal region of freshwater influence (ROFI). A nested version of the SYMPHONIE primitive-equation free-surface model for 3-D baroclinic coastal flows has been developed for the Rhône ROFI. The main characteristics of the model are a generalized sigma coordinate system in finite differences, using a time splitting for external and internal modes and high-order numerical advection schemes for density fields in combination with an modified turbulence closure scheme. The nesting system consists of two grids forced by the high-resolution ALADIN model atmospheric data. The coarse grid of 3 km resolution for the whole Gulf of Lions allows the forcing of the Liguro-Provençal large-scale current when the fine mesh of 1-km resolution is centred on the river mouth of the Grand Rhône. Documented field experiments from the Biodypar 3 field campaign performed during March 1999 are used for validation. Numerical results, CTD profiles and a SPOT TSM visible image are in good agreement concerning the shape and structure of the river plume. Other coastal flow features can be observed from satellite imagery. Computations of realistic situations recover these main secondary structures. Complementary process-oriented runs give an explanation of how the coastal upwelling induced by an inhomogeneous offshore wind is destabilized by the combination of the river plume and along-shelf current-blocking effects. In the end, a factor-separation analysis provides evidence that the locally non-linear effects in momentum contribute to the occurrence of secondary vortices

A 3D unified model to Fluid-Structure Interaction with Block Based Adaptive Mesh Refinement

International audienceWe propose to bring a better understanding of the interaction between an air-water flow and a floating structure by means of a fast accurate numerical model. Following the 3D low Mach compressible Euler model developed in [14] and previous works from [20], [11] and [13], we are now interested in simulating the motion of a floating structure in an air-water flow. In the context of a fictitious domain, a volumic penalization is applied inside the body to ensure a rigidity constraint through a penalized velocity in order to get the correct motion of the rigid body. The tracking of the solid is insured by the reconstruction of a Heaviside function thanks to a ray-casting algorithm. The validity of our fluid-structure interaction (FSI) procedure is investigated through some examples

Generation mechanisms for mesoscale eddies in the Gulf of Lions: radar observation and modeling

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Numerical evaluation of artificial boundary condition for wall-bounded stably stratified flows

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