79 citations · 162 across the 15 of their papers we have counts for
20 papers
Multi-material flow with a new viscoelastic model
S{é}bastien Boyaval
We study a new quasilinear system of balance laws (i.e. conservative first-order PDEs with source terms) for the numerical simulation by a front-capturing approach of viscoelastic…
About the structural stability of Maxwell fluids: convergence toward elastodynamics
Sébastien Boyaval
Maxwell's models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. Bu…
A viscoelastic flow model of Maxwell-type with a symmetric-hyperbolic formulation
Sébastien Boyaval
Maxwell models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But…
Non-isothermal viscoelastic flows with conservation laws and relaxation
Sébastien Boyaval, Mark Dostalík
We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the…
Viscoelastic flows of Maxwell fluids with conservation laws
Sébastien Boyaval
We consider multi-dimensional extensions of Maxwell's seminal rheo-logical equation for 1D viscoelastic flows. We aim at a causal model for compressible flows, defined by semi-grou…
Finite-Volume approximation of the invariant measure of a viscous stochastic scalar conservation law
Sébastien Boyaval, Sofiane Martel, Julien Reygner
We study the numerical approximation of the invariant measure of a viscous scalar conservation law, one-dimensional and periodic in the space variable, and stochastically forced wi…
Viscoelastic flows with conservation laws
Sébastien Boyaval
We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized b…
Reduced basis approximation and a~posteriori error bounds for 4D-Var data assimilation
Mark Kärcher, Sébastien Boyaval, Martin A. Grepl +1
We propose a certified reduced basis approach for the strong- and weak-constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model. Whil…
Derivation and numerical approximation of hyperbolic viscoelastic flow systems: Saint-Venant 2D equations for Maxwell fluids
Sébastien Boyaval
We pursue here the development of models for complex (viscoelastic) fluids in shallow free-surface gravity flows which was initiated by [Bouchut-Boyaval, M3AS (23) 2013] for 1D (tr…
Finite Element Approximation of the FENE-P Model
John Barrett, Sébastien Boyaval
We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polym…
A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids
Sébastien Boyaval
Saint-Venant equations can be generalized to account for a viscoelastic rheology in shallow flows. A Finite-Volume discretization for the 1D Saint-Venant system generalized to Uppe…
Johnson-Segalman -- Saint-Venant equations for viscoelastic shallow flows in the elastic limit
Sébastien Boyaval
The shallow-water equations of Saint-Venant, often used to model the long-wave dynamics of free-surface flows driven by inertia and hydrostatic pressure, can be generalized to acco…
Unified formal reduction for fluid models of free-surface shallow gravity-flows
François Bouchut, Sébastien Boyaval
We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gra…
A fast Monte-Carlo method with a Reduced Basis of Control Variates applied to Uncertainty Propagation and Bayesian Estimation
Sébastien Boyaval
The Reduced-Basis Control-Variate Monte-Carlo method was introduced recently in [S. Boyaval and T. Lelièvre, CMS, 8 2010] as an improved Monte-Carlo method, for the fast estimation…
A new model for shallow viscoelastic fluids
François Bouchut, Sébastien Boyaval
We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for e…
Reduced basis techniques for stochastic problems
Sébastien Boyaval, Claude Le Bris, Tony Lelièvre +3
We report here on the recent application of a now classical general reduction technique, the Reduced-Basis approach initiated in [C. Prud'homme, D. Rovas, K. Veroy, Y. Maday, A. T.…
Existence and approximation of a (regularized) Oldroyd-B model
John W. Barrett, Sebastien Boyaval
Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The…
A Variance Reduction Method for Parametrized Stochastic Differential Equations using the Reduced Basis Paradigm
Sebastien Boyaval, Tony Lelievre
In this work, we develop a reduced-basis approach for the efficient computation of parametrized expected values, for a large number of parameter values, using the control variate m…
Free-energy-dissipative schemes for the Oldroyd-B model
Sébastien Boyaval, Tony Lelièvre, Claude Mangoubi
In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model,…
Reduced-Basis approach for homogenization beyond the periodic setting
Sébastien Boyaval
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large n…