PASQUETTI , Richard

Hyperbolic systems and dispersive equations remain challenging for finite element methods (FEMs). On the basis of an arbitrarily high order FEM, namely the spectral element method (SEM), we address :-The Korteweg-de Vries equation, to explain how high order derivative terms can be efficiently handled with a C0-continuous Galerkin approximation....

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Two viscous stabilization methods, namely the spectral vanishing viscosity (SVV) technique and the entropy viscosity method (EVM), are applied to flows of interest in geophysics. First, following a study restricted to one space dimension, the spectral element approximation of the shallow water equations is stabilized using the EVM. Our recent...

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National audience

Two viscous stabilization methods, namely the spectral vanishing viscosity (SVV) techniqueand the entropy viscosity method (EVM), are applied to flows of interest in geophysics. First,following a study restricted to one space dimension, the spectral element approximation ofthe shallow water equations is stabilized using the EVM. Our recent...

National audience

International audience

Using the spectral element method (SEM), or more generally hp-finite elements, it is possible to solve with high accuracy various kinds of problems governed by partial differential equations (PDEs). However, as soon as the physical domain is not polygonal the accuracy quickly deteriorates if curved elements are not implemented. For the...

In a recent JCP paper (by Y. Liu et al., vol. 336, p. 458, 2017) a higher order triangular spectral element method (T SEM) is proposed to address seismic wave field modeling. The main interest of this T SEM is that the mass matrix is diagonal, so that an explicit time marching becomes very cheap. This property results from the fact that,...

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International audience

Hyperbolic systems and dispersive equations remain challenging for the FEM community. Onthe basis of an arbitrarily high order FEM, namely the spectral element method (SEM), here weaddress:- The Korteweg-de Vries equation, to explain how high order derivative terms can be efficientlyhandled with a C 0 continuous Galerkin...

We present a review in the construction of accurate and efficient multivariate polynomial approximations on elementary domains that are not Cartesian products of intervals, such as triangles and tetrahedra. After the generalities for high-order nodal interpolation of a function over an interval, we introduce collapsed coordinates and warped...

Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field...

To address the so-called Bohm boundary conditions, generally imposed at the walls that intercept in a tokamak the magnetic field lines, we consider a simple one-dimensional hyperbolic system that constitutes a minimal transport model for ionic density and momentum. We show that as soon as the solution is smooth, a spectrally accurate...

We present a review in the construction of accurate and efficient multivariate polynomial approximations on elementary domains that are not Cartesian products of intervals, such as triangles and tetrahedra. After the generalities for high-order nodal interpolation of a function over an interval, we introduce collapsed coordinates and warped...

International audience

International audience

A simple model of synthetic (zero-net mass-flux) micro-jet is proposed and implemented in a large-eddysimulation spectral solver of the incompressible Navier–Stokes equations. Essentially, it is simplyrequired to introduce a penalty like term in the momentum equation, with a variable penalty coefficientthat culminates during the expulsion...

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International audience

We investigate the cubature points based triangular spectral element method and provide accuracy results for elliptic problems in non polygonal domains using various isoparametric mappings. The capabilities of the method are here again clearly confirmed.