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Article
Convergence of the Fully Discrete Incremental Projection Scheme for Incompressible Flows
The present paper addresses the convergence of a first-order in time incremental projection scheme for the time-dependent incompressible Navier–Stokes equations to a weak solution. We prove the convergence of ...
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Article
Lax–Wendroff consistency of finite volume schemes for systems of non linear conservation laws: extension to staggered schemes
We prove in this paper the Lax–Wendroff consistency of a general finite volume convection operator acting on discrete functions which are possibly not piecewise-constant over the cells of the mesh and over the...
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Article
Modelling of a spherical deflagration at constant speed
We build in this paper a numerical solution procedure to compute the flow induced by a spherical flame expanding from a point source at a constant expansion velocity, with an instantaneous chemical reaction. T...
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Chapter
Consistent Internal Energy Based Schemes for the Compressible Euler Equations
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of ...
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Chapter and Conference Paper
A Staggered Pressure Correction Numerical Scheme to Compute a Travelling Reactive Interface in a Partially Premixed Mixture
We address a turbulent deflagration model with a flow governed by the compositional Euler equations and the flame propagation represented by the transport of the characteristic function. The numerical scheme w...
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Chapter and Conference Paper
3-Dimensional Particulate Flow Modelling Using a Viscous Penalty Combined with a Stable Projection Scheme
introduce a strategy for the simulation a particulate flow in a 3-dimensional domain. The particles are assumed to be rigid, and the homogeneous fluid flow to be governed by the incompressible Navier–...
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Chapter and Conference Paper
MUSCL Discretization for the Fluid Flow Convection Operator on Staggered Meshes
propose in this paper a second order discretization of the momentum convection operator for fluid flow simulation on staggered quadrangular or hexahedral meshes. The velocity is approximated by the Rann...
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Chapter and Conference Paper
A Second Order Numerical Scheme for Large-Eddy Simulation of Compressible Flows
the context of large eddy simulation of turbulent flows, the control of kinetic energy seems to be an essential requirement for a numerical scheme. We propose in this paper a formally second order non...
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Chapter and Conference Paper
A Second Order Consistent MAC Scheme for the Shallow Water Equations on Non Uniform Grids
propose in this paper a formally second order scheme for the numerical simulation of the shallow water equations in two space dimensions, based on the so-called Marker-And-Cell (MAC) staggered discret...
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Chapter and Conference Paper
A Marker-and-Cell Scheme for Viscoelastic Flows on Non Uniform Grids
this paper, we develop a numerical scheme for the solution of the coupled Stokes and Navier-Stokes equations with constitutive equations describing the flow of viscoelastic fluids. The space discret...
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Article
On the weak consistency of finite volumes schemes for conservation laws on general meshes
The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, an analogue of the Lax–Wendroff theorem for) finite volume schemes for balance laws in the multi-dimen...
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Article
Convergence of the Marker-and-Cell Scheme for the Incompressible Navier–Stokes Equations on Non-uniform Grids
We prove in this paper the convergence of the Marker-and-Cell scheme for the discretization of the steady-state and time-dependent incompressible Navier–Stokes equations in primitive variables, on non-uniform ...
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Chapter and Conference Paper
Convergence of the MAC Scheme for Variable Density Flows
We prove in paper of an semi-implicit MAC for the time-dependent variable density Navier–Stokes equations.
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Article
Analysis of a fractional-step scheme for the P \(_1\) radiative diffusion model
We address in this paper a non-linear parabolic system, which is built to retain the main mathematical difficulties of the P ...
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Chapter and Conference Paper
Convergence of the MAC Scheme for the Steady-State Incompressible Navier-Stokes Equations on Non-uniform Grids
We prove in this paper the convergence of the Marker and cell (MAC) scheme for the discretization of the steady-state incompressible Navier-Stokes equations in primitive variables on non-uniform Cartesian gri...
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Article
W1,q stability of the Fortin operator for the MAC scheme
We prove in this paper the continuity of the natural projection operator from \(W^{1,q}_{0}(\varOmega )^{d}\) , q∈[1,+∞)...
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Chapter and Conference Paper
Discretization of the viscous dissipation term with the MAC scheme
We propose a discretization for the MAC scheme of the viscous dissipation term τ(u) : Δu (where τ(u) stands for the shear stress tensor associated to the velocity field u), which is suitable to obtain an uncondit...
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Chapter and Conference Paper
Staggered discretizations, pressure correction schemes and all speed barotropic flows
We present in this paper a class of schemes for the solution of the barotropic Navier-Stokes equations. These schemes work on general meshes, preserve the stability properties of the continuous problem, irresp...
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Chapter and Conference Paper
Playing with Burgers’s Equation
The 1D Burgers equation is used as a toy model to mimick the resulting behaviour of numerical schemes when replacing a conservation law by a form which is equivalent for smooth solutions, such as the total ene...
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Chapter and Conference Paper
A Low Degree Non–Conforming Approximation of the Steady Stokes Problem with an Eddy Viscosity
In the context of Large Eddy Simulation, the use of a turbulence model brings the question of the implementation of the eddy–viscosity. In this communication, we propose to assess the discretization of the dif...
