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The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared to each other. They...
The calculation of sound generation and propagation in low
Mach number flows requires serious reflections on the characteristics of the
underlying equations. Although the compressible Euler/Navier-Stokes
equations cover all effects, an approximation via standard compressible
solvers does not have the ability to represent acoustic waves
correctly. Therefore, different methods have been developed to deal with the
problem. In this paper, three of them are considered and compared to each
other....
This article is devoted to incompressible Euler equations (or to Navier-Stokes equations in the vanishing viscosity limit). It describes the propagation of quasi-singularities. The underlying phenomena are consistent with the notion of a cascade of energy.
We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor , where the nonlinear function satisfies or . First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for for both models. Then, under vanishing higher viscosity , the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for , its uniqueness and...
In this work we introduce a new class of lowest order methods for diffusive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise affine polynomial space with optimal approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point finite volume methods, although we use them in a rather different context. The incomplete polynomial space replaces classical complete polynomial spaces in discrete...
In this work we introduce a new class of lowest order methods for
diffusive problems on general meshes with only one unknown per
element.
The underlying idea is to construct an incomplete piecewise affine
polynomial space with optimal approximation properties starting
from values at cell centers.
To do so we borrow ideas from multi-point finite volume methods,
although we use them in a rather different context.
The incomplete polynomial space replaces classical complete
polynomial spaces...
We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes...
We present one- and two-dimensional central-upwind schemes
for approximating solutions of the Saint-Venant system
with source terms due to bottom topography.
The Saint-Venant system has steady-state solutions
in which nonzero flux gradients are exactly balanced by
the source terms. It is a challenging problem to preserve
this delicate balance with numerical schemes.
Small perturbations of these states are also very difficult
to compute. Our approach is based on extending semi-discrete central...
In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.
In this paper we show how abstract physical requirements are enough
to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.
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