Search results for "Euler"
showing 10 items of 159 documents
Euler characteristic formulas for simplicial maps
2001
In this paper, various Euler characteristic formulas for simplicial maps are obtained, which generalize the Izumiya–Marar formula [ 14 ], the Banchoff triple point formula [ 3 ] and the formula due to Szucs for maps of surfaces into 3-space [ 27 ]. Moreover, we obtain new results about the Euler characteristics of the multiple point sets and the images of generic smooth maps and the numbers of their singularities.
Inertial modes in stratified rotating neutron stars : An evolutionary description
2005
With (non-barotropic) equations of state valid even when the neutron, proton and electron content of neutron star cores is not in beta equilibrium, we study inertial and composition gravity modes of relativistic rotating neutron stars. We solve the relativistic Euler equations in the time domain with a three dimensional numerical code based on spectral methods, in the slow rotation, relativistic Cowling and anelastic approximations. Principally, after a short description of the gravity modes due to smooth composition gradients, we focus our analysis on the question of how the inertial modes are affected by non-barotropicity of the nuclear matter. In our study, the deviation with respect to …
Euler integral as a source of chaos in the three–body problem
2022
In this paper we address, from a purely numerical point of view, the question, raised in [20, 21], and partly considered in [22, 9, 3], whether a certain function, referred to as "Euler Integral", is a quasi-integral along the trajectories of the three-body problem. Differently from our previous investigations, here we focus on the region of the "unperturbed separatrix", which turns to be complicated by a collision singularity. Concretely, we reduce the Hamiltonian to two degrees of freedom and, after fixing some energy level, we discuss in detail the resulting three-dimensional phase space around an elliptic and an hyperbolic periodic orbit. After measuring the strength of variation of the…
Numerical approximation of the viscous quantum hydrodynamic model for semiconductors
2006
The viscous quantum hydrodynamic equations for semiconductors with constant temperature are numerically studied. The model consists of the one-dimensional Euler equations for the electron density and current density, including a quantum correction and viscous terms, coupled to the Poisson equation for the electrostatic potential. The equations can be derived formally from a Wigner-Fokker-Planck model by a moment method. Two different numerical techniques are used: a hyperbolic relaxation scheme and a central finite-difference method. By simulating a ballistic diode and a resonant tunneling diode, it is shown that numerical or physical viscosity changes significantly the behavior of the solu…
Power ENO methods: a fifth-order accurate Weighted Power ENO method
2004
In this paper we introduce a new class of ENO reconstruction procedures, the Power ENO methods, to design high-order accurate shock capturing methods for hyperbolic conservation laws, based on an extended class of limiters, improving the behavior near discontinuities with respect to the classical ENO methods. Power ENO methods are defined as a correction of classical ENO methods [J. Comput. Phys. 71 (1987) 231], by applying the new limiters on second-order differences or higher. The new class of limiters includes as a particular case the minmod limiter and the harmonic limiter used for the design of the PHM methods [see SIAM J. Sci. Comput. 15 (1994) 892]. The main features of these new ENO…
Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
2017
In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization t…
Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments
2013
Accepted by the Journal of Computational Physics Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a Discontinuous Galerkin method. Time integration is done with an IMEXmethod and the dy…
A marching in space and time (MAST) solver of the shallow water equations. Part II: The 2D model
2007
Abstract A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are…
Prediction of flow patterns during silo discharges using a finite element approach and its preliminary experimental verification
2015
Abstract Obtaining a reliable discharge of particulate solids from a storage silo is a prerequisite to securing operational adequacy in solids handling processes. If a silo is poorly designed, an unreliable interrupted discharge often occurs. In this study, an in-house finite element (FE) program was modified to predict the particulate solids flow patterns during discharges from silos, and the effect of a double-cone insert on such flow patterns. In FE modeling, a Eulerian approach was adopted with an assumption of steady-state flow—a state that greatly facilitated investigations on the effects of double-cone inserts on the flow of particulate solids. Predictions were carried out on whether…
Analysis of a Parabolic Cross-Diffusion Semiconductor Model with Electron-Hole Scattering
2007
The global-in-time existence of non-negative solutions to a parabolic strongly coupled system with mixed Dirichlet–Neumann boundary conditions is shown. The system describes the time evolution of the electron and hole densities in a semiconductor when electron-hole scattering is taken into account. The parabolic equations are coupled to the Poisson equation for the electrostatic potential. Written in the quasi-Fermi potential variables, the diffusion matrix of the parabolic system contains strong cross-diffusion terms and is only positive semi-definite such that the problem is formally of degenerate type. The existence proof is based on the study of a fully discretized version of the system…