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Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined the
wind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFD
has had its most favorable impact on the aerodynamic design of the high-speed cruise
configuration of a transport. This success has raised expectations among aerodynamicists
that the applicability of CFD can be extended to the full flight envelope. However, the
complex nature...
A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity...
We present and analyse in this paper a novel colocated Finite Volume scheme for the solution of the Stokes problem.
It has been developed following two main ideas.
On one hand, the discretization of the pressure gradient term is built as the discrete transposed of the velocity divergence term, the latter being evaluated using a natural finite volume approximation; this leads to a non-standard interpolation formula for the expression of the pressure on the edges of the control volumes.
On the other...
We consider the local projection finite element method for the discretization of a scalar convection-diffusion equation with a divergence-free convection field. We introduce a new fluctuation operator which is defined using an orthogonal projection with respect to a weighted inner product. We prove that the bilinear form corresponding to the discrete problem satisfies an inf-sup condition with respect to the SUPG norm and derive an error estimate for the discrete solution.
Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.
We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order in the -norm for sufficiently smooth functions.
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
The Schwarz alternating method can be used to solve
elliptic boundary value problems on domains which consist of two or more
overlapping subdomains. The solution is approximated by an infinite sequence of
functions which results from solving a sequence of elliptic boundary value
problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for
nonlinear elliptic problems which are known to have solutions by the monotone
method (also known as the method...
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
In this paper, a Dirichlet-Neumann substructuring domain
decomposition method is presented for a finite element
approximation to the nonlinear Navier-Stokes equations. It is
shown that the Dirichlet-Neumann domain decomposition sequence
converges geometrically to the true solution provided the Reynolds
number is sufficiently small. In this method, subdomain problems
are linear. Other version where the subdomain problems are linear
Stokes problems is also presented.
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...
We are interested in the numerical solution of a two-dimensional fluid-structure interaction problem. A special attention is paid to the choice of physically relevant inlet boundary conditions for the case of channel closing. Three types of the inlet boundary conditions are considered. Beside the classical Dirichlet and the do-nothing boundary conditions also a generalized boundary condition motivated by the penalization prescription of the Dirichlet boundary condition is applied. The fluid flow...
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