A general class of phase transition models with weighted interface energy
A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids
The newly developed unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form....
A high-precision algorithm for axisymmetric flow.
A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport
The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different HLLC solvers. Some results concerning the non-negativity...
A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport
The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different...
A hybrid multigrid method for the steady-state incompressible Navier-Stokes equations.
A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems
The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density and additional...
A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems
The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density...
A mathematical model for core-annular fluids with surfactants.
A mathematical model for resin transfer molding
A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration
In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.
A Mixed Finite Element Approximation of the Navier-Stokes Equations.
A mixed formulation of a sharp interface model of stokes flow with moving contact lines
Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking...
A modified Cayley transform for the discretized Navier-Stokes equations
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform of the...
A Multidimensional fluctuation splitting scheme for the three dimensional Euler equations
A multidimensional fluctuation splitting scheme for the three dimensional Euler equations
The fluctuation splitting schemes were introduced by Roe in the beginning of the 80's and have been then developed since then, essentially thanks to Deconinck. In this paper, the fluctuation splitting schemes formalism is recalled. Then, the hyperbolic/elliptic decomposition of the three dimensional Euler equations is presented. This decomposition leads to an acoustic subsystem and two scalar advection equations, one of them being the entropy advection. Thanks to this decomposition, the two scalar...
A multidomain spectral collocation method for the Stokes problem.
A multigrid method for a Petrov-Galerkin discretization of the Stokes equations.
A multigrid smoother for high Reynolds number flows.
A multilevel method of nonlinear Galerkin type for the Navier-Stokes equations.