Some implementations of projection methods for Navier-Stokes equations
Some New Families of Finite Elements for the Stokes Equations.
Some special solutions of self similar type in MHD, obtained by a separation method of variables
Some special solutions of self similar type in MHD, obtained by a separation method of variables
We use a method based on a separation of variables for solving a first order partial differential equations system, using a very simple modelling of MHD. The method consists in introducing three unknown variables Φ1, Φ2, Φ3 in addition to the time variable t and then in searching a solution which is separated with respect to Φ1 and t only. This is allowed by a very simple relation, called a “metric separation equation”, which governs the type of solutions with respect to time. The families...
Space-time variational saddle point formulations of Stokes and Navier–Stokes equations
The instationary Stokes and Navier−Stokes equations are considered in a simultaneously space-time variational saddle point formulation, so involving both velocities u and pressure p. For the instationary Stokes problem, it is shown that the corresponding operator is a boundedly invertible linear mapping between H1 and H'2, both Hilbert spaces H1 and H2 being Cartesian products of (intersections of) Bochner spaces, or duals of those. Based on these results, the operator that corresponds to the Navier−Stokes...
Spatially-dependent and nonlinear fluid transport: coupling framework
We introduce a solver method for spatially dependent and nonlinear fluid transport. The motivation is from transport processes in porous media (e.g., waste disposal and chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas. The main idea is to apply transformation methods to spatial and nonlinear terms to obtain linear or nonlinear ordinary differential equations. Such differential equations can be simply solved with Laplace transformation...
Special finite-difference approximations of flow equations in terms of stream function, vorticity and velocity components for viscous incompressible liquid in curvilinear orthogonal coordinates
The Navier-Stokes equations written in general orthogonal curvilinear coordinates are reformulated with the use of the stream function, vorticity and velocity components. The resulting system id discretized on general irregular meshes and special monotone finite-difference schemes are derived.
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...
Spectral element simulations of flow past an ellipsoid at different Reynolds numbers.
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct...
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [CITE] and show that the kernel modes that define the spectral method have the correct...
Spectral Numerical Study of a Problem Governed by Navier-Stokes Equations, Influence of Rayleigh and Prandtl Numbers
We present in this work a numerical study of a problem governed by Navier-Stokes equations and heat equation. The mathematical problem under consideration is obtained by modelling the natural convection of an incompressible fluid, in laminar flow between two horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed to be greater than the outer one. The numerical simulation of the flow is carried out by collocation-Legendre...
Spectral-finite element method for compressible fluid flows
Stability analysis of shallow wake flows with free surface.
Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation
We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.
Stability and Convergence of the Difference Schemes for Equations of Isentropic Gas Dynamics in Lagrangian Coordinates
Stability and numerical analysis of the Hébraud-Lequeux model for suspensions.
Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations
We consider some abstract nonlinear equations in a separable Hilbert space and some class of approximate equations on closed linear subspaces of . The main result concerns stability with respect to the approximation of the space . We prove that, generically, the set of all solutions of the exact equation is the limit in the sense of the Hausdorff metric over of the sets of approximate solutions, over some filterbase on the family of all closed linear subspaces of . The abstract results are...
Stability of a finite element method for 3D exterior stationary Navier-Stokes flows
We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary....