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Displaying 241 –
260 of
512
This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done using an L-stable Runge−Kutta scheme. The convergence of the method is shown to be independent of the anisotropy parameter , and this for fixed...
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
In this paper we present a methodology for constructing accurate
and efficient hybrid central-upwind (HCU) type schemes for
the numerical resolution of a two-fluid model commonly used by the
nuclear and petroleum industry. Particularly, we propose a method
which does not make use of any information about the
eigenstructure of the Jacobian matrix of the model.
The two-fluid model possesses a highly nonlinear pressure law.
From the mass conservation equations we develop an evolution
equation which...
In this work we describe an efficient model for the simulation of a
two-phase flow made of a gas and a granular solid. The starting point is the two-velocity
two-pressure model of Baer and Nunziato
[Int. J. Multiph. Flow16 (1986) 861–889].
The model is supplemented by
a relaxation source term in order
to take into account the pressure equilibrium between the two phases and
the granular stress in the solid phase. We show that the relaxation
process can be made thermodynamically coherent with an...
Classical solutions of quasilinear functional differential equations are approximated with solutions of implicit difference schemes. Proofs of convergence of the difference methods are based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions are used. Numerical examples are given.
Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.
We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...
We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...
We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...
We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central
discontinuous Galerkin method and the regular discontinuous
Galerkin method in this context is also made.
Numerical experiments are provided to validate the quantitative
conclusions from the analysis.
We investigate sufficient and possibly
necessary conditions for the L2 stability of the upwind first order
finite volume scheme for Maxwell equations, with metallic and
absorbing boundary conditions. We yield a very general sufficient condition,
valid for any finite volume partition in two and three space
dimensions. We show this condition is necessary for a class of
regular meshes in two space dimensions. However, numerical tests show
it is not necessary
in three space dimensions even on regular...
The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part of the boundary is studied in this paper. The problem is discretized in space by the finite element method with linear functions on triangular elements and in time by the implicit-explicit method (the left-hand side by the implicit Euler method and the right-hand...
Currently displaying 241 –
260 of
512