1,558 research outputs found
Steady state spurious errors in shock-capturing numerical schemes
The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows
A convergent nonconforming finite element method for compressible Stokes flow
We propose a nonconforming finite element method for isentropic viscous gas
flow in situations where convective effects may be neglected. We approximate
the continuity equation by a piecewise constant discontinuous Galerkin method.
The velocity (momentum) equation is approximated by a finite element method on
div-curl form using the nonconforming Crouzeix-Raviart space. Our main result
is that the finite element method converges to a weak solution. The main
challenge is to demonstrate the strong convergence of the density
approximations, which is mandatory in view of the nonlinear pressure function.
The analysis makes use of a higher integrability estimate on the density
approximations, an equation for the "effective viscous flux", and renormalized
versions of the discontinuous Galerkin method.Comment: 23 page
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Material Issues of the Metal Printing Process, MPP
The metal printing process, MPP; is a novel Rapid Manufacturing process under development
at SINTEF and NTNU in Trondheim, Norway. The process, which aims at the manufacturing
of end-use products for demanding applications in metallic and CerMet materials, consists of
two separate parts; The layer fabrication, based on electrostatic attraction of powder materials,
and the consolidation, consisting of the compression and sintering of each layer in a heated
die. This approach leads to a number of issues regarding the interaction between the process
solutions and the materials. This paper addresses some of the most critical material issues at
the current development stage of MPP, and the present solutions to these.Mechanical Engineerin
Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation
We consider conservation laws with source terms in a bounded domain with
Dirichlet boundary conditions. We first prove the existence of a strong trace
at the boundary in order to provide a simple formulation of the entropy
boundary condition. Equipped with this formulation, we go on to establish the
well-posedness of entropy solutions to the initial-boundary value problem. The
proof utilizes the kinetic formulation and the compensated compactness method.
Finally, we make use of these results to demonstrate the well-posedness in a
class of discontinuous solutions to the initial-boundary value problem for the
Degasperis-Procesi shallow water equation, which is a third order nonlinear
dispersive equation that can be rewritten in the form of a nonlinear
conservation law with a nonlocal source term.Comment: 24 page
Well-posedness results for triply nonlinear degenerate parabolic equations
We study the well-posedness of triply nonlinear degenerate
elliptic-parabolic-hyperbolic problem in a bounded domain with
homogeneous Dirichlet boundary conditions. The nonlinearities and
are supposed to be continuous non-decreasing, and the nonlinearity
falls within the Leray-Lions framework. Some restrictions
are imposed on the dependence of on
and also on the set where degenerates. A model case is
with which is strictly increasing except on a locally finite number of
segments, and which is of the Leray-Lions kind. We are
interested in existence, uniqueness and stability of entropy solutions. If
, we obtain a general continuous dependence result on data
and nonlinearities . Similar result
is shown for the degenerate elliptic problem which corresponds to the case of
and general non-decreasing surjective . Existence, uniqueness
and continuous dependence on data are shown when and
is continuous
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