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Displaying 201 –
220 of
262
In this paper, we propose implicit and semi-implicit in time finite volume schemes for the barotropic Euler equations (hence, as a particular case, for the shallow water equations) and for the full Euler equations, based on staggered discretizations. For structured meshes, we use the MAC finite volume scheme, and, for general mixed quadrangular/hexahedral and simplicial meshes, we use the discrete unknowns of the Rannacher−Turek or Crouzeix−Raviart finite elements. We first show that a solution...
It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of th order accuracy in the energy norm called elements. For we show that the stability condition holds if the velocity...
The LBB condition is well-known to guarantee the stability of a finite
element (FE) velocity - pressure pair in incompressible flow calculations.
To ensure the condition to be satisfied a certain constant should be positive and
mesh-independent. The paper studies the dependence of the LBB condition on the
domain geometry. For model domains such as strips and rings the
substantial dependence of this constant on geometry aspect ratios is observed.
In domains with highly anisotropic substructures...
We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss...
We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in...
We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with . These equations also modelize
the shallow water problem in height-flow rate formulation used to
solve the flow in lakes and perfectly well-mixed sea. We establish
a convergence result for the time-discretized problem when the
momentum equation and the continuity equation are solved with the
Galerkin method, without adding a penalization term in the
continuity equation as it is made in Lions...
We present a numerical simulation of two coupled Navier-Stokes flows, using ope-rator-split-ting and optimization-based non-overlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid...
The one-dimensional steady-state convection-diffusion problem for the unknown temperature of a medium entering the interval with the temperature and flowing with a positive velocity is studied. The medium is being heated with an intensity corresponding to for a constant . We are looking for a velocity with a given average such that the outflow temperature is maximal and discuss the influence of the boundary condition at the point on the “maximizing” function .
We consider a finite element discretization by
the Taylor–Hood element for the stationary
Stokes and Navier–Stokes
equations with slip boundary condition. The slip boundary condition
is enforced pointwise for nodal values of the velocity in
boundary nodes. We prove optimal error estimates in the
H1 and L2 norms for the velocity and pressure respectively.
We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example...
We consider the analysis and
numerical solution of a forward-backward boundary value problem.
We provide some motivation, prove existence and uniqueness in a function
class especially geared to the problem at hand, provide various energy
estimates, prove a priori error estimates for the Galerkin method,
and show the results of some numerical computations.
We study the 2D magnetohydrodynamic (MHD) equations for a viscous incompressible resistive fluid, a system with the Navier-Stokes equations for the velocity field coupled with a convection-diffusion equation for the magnetic fields, in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality with a large class of non-autonomous external forces. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal...
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262