Spectral methods for kinetic theory models of viscoelastic fluids
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The goal of this project is to numerically solve the Navier-Stokes equations by using different numerical methods with particular emphasis on solving the problem of the flow past a square cylinder. In particular, we use the finite element method based on P ...
Isogeometric analysis (IGA) is a computational methodology recently developed to numerically approximate Partial Differential Equation (PDEs). It is based on the isogeometric paradigm, for which the same basis functions used to represent the geometry are t ...
We investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al. (Phys. Rev. Lett., vol. 107 (18), 2011, 188301). The fricti ...
In this article we propose a stochastic bed load transport formulation within the framework of the frictional shallow-water equations in which the sediment transport rate results from the difference between the entrainment and deposition of particles. Firs ...
In this paper we provide a general framework for model reduction methods applied to fluid flow in porous media. Using reduced basis and numerical homogenization techniques we show that the complexity of the numerical approximation of Stokes flow in heterog ...
We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...
Society for Industrial and Applied Mathematics2014
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...
A numerical method for the solution to the density-dependent incompressible Navier-Stokes equations modeling the flow of N immiscible incompressible liquid phases with a free surface is proposed. It allows to model the flow of an arbitrary number of liquid ...
Shedding of droplets in a flow focusing junction is standard technique in two-phase microfluidics. This break-up is driven by a capillary instability. Here we present a depth-averaged approach to simulate these complex phenomena. Since the physical mechani ...
A linear and spectral model has recently been developed [1], describing the self-consistent wave-particle interaction in a gyrotron oscillator. The spectral approach, compared to commonly used time-evolution approaches, has the possibility to describe all ...