A convergent staggered scheme for the variable density incompressible Navier-Stokes equations

@article{Latch2018ACS,
  title={A convergent staggered scheme for the variable density incompressible Navier-Stokes equations},
  author={Jean-Claude Latch{\'e} and Khaled Saleh},
  journal={Math. Comput.},
  year={2018},
  volume={87},
  pages={581-632}
}
In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the so-called Rannacher-Turek element. The convection term in the momentum balance equation is discretized by a finite volume technique, in such a way that a solution obeys a discrete kinetic energy balance, and the mass balance is approximated by an upwind finite volume… 

Figures from this paper

A discrete kinetic energy preserving convection operator for variable density flows on locally refined staggered meshes
TLDR
This paper builds and analyzes a scheme for the time-dependent variable density Navier-Stokes equations, able to cope with unstructured non-conforming meshes, with hanging nodes, and theoretically establishes a first order convergence in space for energy norms.
A convergent FV-FEM scheme for the stationary compressible Navier-Stokes equations
TLDR
This paper proposes a discretization of the multi-dimensional stationary compressible Navier-Stokes equations combining finite element and finite volume techniques and shows the first convergence result for a numerical method with adiabatic exponents less than 3 when the space dimension is three.
A Class of Staggered Schemes for the Compressible Euler Equations
TLDR
A class of numerical schemes for the solution of the Euler equations based on staggered discretizations and work either on structured meshes or on general simplicial or tetrahedral/hexahedral meshes, achieving the consistency in the Lax-Wendroff sense.
A cell-centred pressure-correction scheme for the compressible Euler equations
We propose a robust pressure-correction scheme for the numerical solution of the compressible Euler equations discretized by a collocated finite volume method. The scheme is based on an internal
Low Mach number limit of some staggered schemes for compressible barotropic flows
TLDR
It is rigorously proved that for a given mesh and a given time step, a sequence of solutions obtained with a sequences of vanishing Mach numbers tend to a solution of a standard scheme for incompressible flows.
J ul 2 01 9 A CONVERGENT FV – FEM SCHEME FOR THE STATIONARY COMPRESSIBLE NAVIER-STOKES EQUATIONS
In this paper, we propose a discretization of the multi-dimensional stationary compressible Navier-Stokes equations combining finite element and finite volume techniques. As the mesh size tends to 0,
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
A convergent FV–FE scheme for the stationary compressible Navier–Stokes equations
In this paper we prove a convergence result for a discretization of the three-dimensional stationary compressible Navier–Stokes equations assuming an ideal gas pressure law $p(\rho )=a \rho
The second-order stabilized Gauge-Uzawa method for incompressible flows with variable density
The Navier-Stokes equations with variable density are challenging problems in numerical analysis community. We recently built the 2nd order stabilized Gauge-Uzawa method [SGUM] to solve the
...
...

References

SHOWING 1-10 OF 45 REFERENCES
An unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equations
In this paper we present a pressure correction scheme for the compressible Navier-Stokes equations. The space discretization is staggered, using either the Marker-And Cell (MAC) scheme for structured
An unconditionnally stable pressure correction scheme for compressible barotropic Navier-Stokes equations
We present in this paper a pressure correction scheme for barotropic compressible NavierStokes equations, which enjoys an unconditional stability property, in the sense that the energy and
A Staggered Scheme with Non-conforming Refinement for the Navier-Stokes Equations
We propose a numerical scheme for the incompressible Navier-Stokes equations. The pressure is approximated at the cell centers while the vector valued velocity degrees of freedom are localized at the
An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model
We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the
An L2‐stable approximation of the Navier–Stokes convection operator for low‐order non‐conforming finite elements
We develop in this paper a discretization for the convection term in variable density unstationary Navier–Stokes equations, which applies to low‐order non‐conforming finite element approximations
A nonconforming finite element method of upstream type applied to the stationary Navier-Stokes equation
— We present a nonconforming finite element method with an upstream discretizatwn of the convective term for solving the stationary Navier-Stokes équations. The existence of at least one solution of
Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes
This paper is devoted to the study of an error estimate of the finite volume approximation to the solution u E L∞(R N × R) of the equation u t + div(v f(u)) = 0, where v is a vector function
...
...