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We study a depth-averaged model of gravity-driven flows made of
solid grains and fluid, moving over variable basal surface.
In particular, we are interested in applications
to geophysical flows such as avalanches and debris flows,
which typically contain both solid material and interstitial fluid.
The model system consists of mass and momentum balance equations for the
solid and fluid components, coupled together by both
conservative and non-conservative terms involving the derivatives of the...
We build a non-dissipative second order algorithm for the approximate resolution of the
one-dimensional Euler system of compressible gas dynamics with two components. The
considered model was proposed in [1]. The algorithm is based on [8] which deals with a
non-dissipative first order resolution in Lagrange-remap formalism. In the present paper
we describe, in the same framework, an algorithm that is second order accurate in time and
space, and that...
We propose an unconditionally stable semi-implicit time discretization of the phase field crystal evolution. It is based on splitting the underlying energy into convex and concave parts and then performing H-1 gradient descent steps implicitly for the former and explicitly for the latter. The splitting is effected in such a way that the resulting equations are linear in each time step and allow an extremely simple implementation and efficient solution. We provide the associated stability and error...
A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is...
The paper deals with the application of a non-conforming domain
decomposition method
to the problem of the computation of induced currents in electric engines
with moving conductors.
The eddy currents model is considered as a quasi-static
approximation of Maxwell
equations and we study its two-dimensional formulation with either the
modified magnetic vector potential or the magnetic field as primary variable.
Two discretizations are proposed, the first one based on curved finite
elements
and the...
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an strategy is employed for approximating the Caputo fractional derivative in the temporal direction, compact CCD finite difference approaches are incorporated in the space. A highly effective hybrid -CCD method is implemented successfully. The accuracy of this linearized scheme is order six in space, and order in time, where is the order of the Caputo fractional derivative involved. It...
In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.
In this paper we solve the time-dependent incompressible Navier-Stokes
equations by splitting the non-linearity and incompressibility, and
using discontinuous or continuous finite element methods in space. We
prove optimal error estimates for the velocity and suboptimal
estimates for the pressure. We present some numerical experiments.
We present in this paper a stability study concerning finite volume schemes
applied to the two-dimensional Maxwell system, using rectangular or triangular
meshes. A stability condition is proved for the
first-order upwind scheme on a rectangular mesh. Stability comparisons
between the Yee scheme and the finite volume formulation are proposed.
We also compare the stability domains obtained when considering the
Maxwell system and the convection equation.
We propose a simple numerical method for capturing the steady state solution of hyperbolic systems with geometrical source terms. We use the interface value, rather than the cell-averages, for the source terms that balance the nonlinear convection at the cell interface, allowing the numerical capturing of the steady state with a formal high order accuracy. This method applies to Godunov or Roe type upwind methods but requires no modification of the Riemann solver. Numerical experiments on scalar...
We propose a simple numerical method for capturing the
steady state solution of hyperbolic systems with geometrical
source terms. We use
the interface value, rather than the cell-averages,
for the source terms that balance the nonlinear convection
at the cell interface, allowing the numerical capturing of the steady
state with a formal high order accuracy. This method applies to Godunov
or Roe type upwind methods but
requires no modification of the Riemann solver.
Numerical experiments on scalar...
The paper investigates the Galerkin method for an initial boundary value problem for heat convection equations. New error estimates for the approximate solutions and their derivatives in strong norm are obtained.
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