Euler System Research Articles

Numerical Analysis of an SEIR Epidemic Model

This paper is concerned for the numerical methods of susceptible exposed infectious recovered (SEIR) epidemic model of Coronavirus disease factor. The model is handled numerically with three extraordinary numerical scheme, forward Euler, Runge-Kutta Plan (RK-4) and the proposed non-standard finite difference (NSFD) techniques. In epidemic model of infectious illnesses, energy is a demon omen property of the consistent framework since negative worth of a subpopulation is useless. The NSFD technique ends up being more important and trustable numerical system than forward Euler and RK-4 strategies. NSFD technique uses terrifically significant properties of tireless SEIR Coronavirus scourge model like energy and presence of equilibria while forward Euler and RK-4 systems can't hold these characteristics. Furthermore, the proposed NSFD is liberated from time step size while forward Euler and RK-4 depend upon the time step size. The numerical diversions with the aid of a numerical test is presented for the endorsements of the huge number of characteristics.

Newtonian Limits and Global Stability of Shock Solutions for Piston Problem to the Relativistic Full Euler System

We are concerned with a one-dimensional piston problem to the compressible relativistic full Euler system when the piston is drawn forward relatively. Given some small perturbations of the piston speed and the initial state, we establish the global structural stability of large shock solutions to the piston problem and also study Newtonian limits as the ratio between the speeds of the flow and the light goes to zero. Furthermore, the long time behavior of shock solutions has been investigated.

Sonic-supersonic jet flows from a two-dimensional nozzle

We present a mathematical analysis for sonic-supersonic jet flows exhausting into a vacuum (and an atmosphere) from a two-dimensional (2D) nozzle. We assume that the flow is governed by the 2D steady Euler system and the state of the flow is given at the exit of the nozzle. When the nozzle is surrounded by a vacuum, the global existence of locally Lipschitz continuous sonic-supersonic jet flows expanding into the vacuum from the nozzle is established. When the nozzle is surrounded by a static atmosphere with a lower pressure than the pressure of the flow at the exit of the nozzle, the local existence of sonic-supersonic jet flows exhausting into the atmosphere is established.

The non-uniqueness of admissible solutions to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint

We investigate the uniqueness of entropy solution to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint. The constraint is imposed with a singular pressure. Given initial data for which the standard self-similar solution consists of one shock or one shock and one rarefaction wave, it turns out that there exist infinitely many admissible weak solutions. This extends the result of Markfelder and Klingenberg in [S. Markfelder and C. Klingenberg, The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock, Arch. Ration. Mech. Anal. 227(3) (2018) 967–994] for classical Euler system to the case with maximum density constraint. Also some estimates on the density of these solutions are given to describe the behavior of solutions near congestion.

Nonlinear Stability of the Bipolar Navier-Stokes-Poisson System with Boundary

The combined quasineutral and zero-viscosity limits of the bipolar Navier-Stokes-Poisson system with boundary are rigorously proved by establishing the nonlinear stability of the approximate solutions. Based on the conormal energy estimates, we showed that the solutions for the original system converge strongly in H 3 space towards the solutions of the one-fluid compressible Euler system as long as the amplitude of the boundary layers is small enough.

Parabolicity of Degenerate Singularities in Axisymmetric Euler Systems with a Gyrostat

Parabolicity of Degenerate Singularities in Axisymmetric Euler Systems with a Gyrostat

A higher rank Euler system for Gm over a totally real field

In this paper, we construct a higher rank Euler system for $\\Bbb\{G\}_m$ over a totally real field by using Stickelberger elements. A key ingredient of the construction is to generalize the notion of the characteristic ideal. Under certain technical assumptions, we prove that all higher Fitting ideals of a certain $p$-ramified Iwasawa module are described by analytic invariants canonicallyassociated with Stickelberger elements.

Kinematics modeling of six degrees of freedom humanoid robot arm using improved damped least squares for visual grasping

<span lang="EN-US">The robotic arm has functioned as an arm in the humanoid robot and is generally used to perform grasping tasks. Accordingly, kinematics modeling both forward and inverse kinematics is required to calculate the end-effector position in the cartesian space before performing grasping activities. This research presents the kinematics modeling of six degrees of freedom (6-DOF) robotic arm of the T-FLoW humanoid robot for the grasping mechanism of visual grasping systems on the robot operating system (ROS) platform and CoppeliaSim. Kinematic singularity is a common problem in the inverse kinematics model of robots, but. However, other problems are mechanical limitations and computational time. The work uses the homogeneous transformation matrix (HTM) based on the Euler system of the robot for the forward kinematics and demonstrates the capability of an improved damped least squares (I-DLS) method for the inverse kinematics. The I-DLS method was obtained by improving the original DLS method with the joint limits and clamping techniques. The I-DLS performs better than the original DLS during the experiments yet increases the calculation iteration by 10.95%, with a maximum error position between the end-effector and target positions in path planning of 0.1 cm.</span>

Singular Limit for the Compressible Navier–Stokes Equations with the Hard Sphere Pressure Law on Expanding Domains

The article is devoted to the asymptotic limit of the compressible Navier–Stokes system with a pressure obeying a hard–sphere equation of state on a domain expanding to the whole physical space $$\textbf{R}^3$$ . Under the assumptions that acoustic waves generated in the case of ill-prepared data do not reach the boundary of the expanding domain in the given time interval and a certain relation between the Reynolds and Mach numbers and the radius of the expanding domain we prove that the target system is the incompressible Euler system on $$\textbf{R}^3$$ . We also provide an estimate of the rate of convergence expressed in terms of characteristic numbers and the radius of domains.

“A posteriori” limited high order and robust schemes for transient simulations of fluid flows in gas dynamics

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of our method is to allow an approximation with a high-order of accuracy in smooth regions of the flow, while ensuring robustness and a non-oscillatory behaviour in the regions of steep gradients, in particular across shocks.Following the Multidimensional Optimal Order Detection (MOOD) ([15,17]) approach, a candidate solution is computed at a next time level via a high-order accurate explicit scheme ([3,5]). A so-called detector determines if the candidate solution reveals any spurious oscillations or numerical issue and, if so, only the troubled cells are locally recomputed via a more dissipative scheme. This allows to design a family of “a posteriori” limited, robust and positivity preserving, as well as high accurate, non-oscillatory and effective scheme. Among the detecting criteria of the novel MOOD strategy, two different approaches from literature, based on the work of [15,17] and on [35], are investigated. Numerical examples in 1D and 2D, on structured and unstructured meshes, are proposed to assess the effective order of accuracy for smooth flows, the non-oscillatory behaviour on shocked flows, the robustness and positivity preservation on more extreme flows.

Global-in-time classical solutions to two-dimensional axisymmetric Euler system with swirl

Global-in-time classical solutions to two-dimensional axisymmetric Euler system with swirl

Vanishing viscosity limit of incompressible flow around a small obstacle: A special case

<abstract><p>In this paper, we consider two dimensional viscous flow around a small obstacle. In <sup>[<xref ref-type="bibr" rid="b4">4</xref>]</sup>, the authors proved that the solutions of the Navier-Stokes system around a small obstacle of size $ \varepsilon $ converge to solutions of the Euler system in the whole space under the condition that the size of the obstacle $ \varepsilon $ is smaller than a suitable constant $ K $ times the kinematic viscosity $ \nu $. We show that, if the Euler flow is antisymmetric, then this smallness condition can be removed.</p></abstract>

Topological analysis of pseudo-Euclidean Euler top for special values of the parameters

An analogue of the Euler top is considered for a pseudo-Euclidean space is under consideration. In the cases when the geometric integral or area integral vanishes the bifurcation diagrams of the moment map are constructed and the homeomorphism class of each leaf of the Liouville foliation is determined. For each arc of the bifurcation diagram, for one of the two possible cases of the mutual arrangement of the moments of inertia, the types of singularities in the preimage of a small neighbourhood of this arc (analogues of Fomenko 3-atoms) are determined, and for nonsingular isoenergy and isointegral surfaces an invariant of rough Liouville equivalence (an analogue of a rough molecule) is constructed. The pseudo-Euclidean Euler system turns out to have noncompact noncritical bifurcations. Bibliography: 23 titles.

Analysis of Self-Similar Solutions of Euler System: SIB, Desingulatization and Impasse Points

Analysis of Self-Similar Solutions of Euler System: SIB, Desingulatization and Impasse Points

Decay rate to contact discontinuities for the one-dimensional compressible Euler-Fourier system with a reacting mixture

In this paper, we investigate the nonlinear stability of contact waves to the Cauchy problem of the compressible Euler-Fourier system with a reacting mixture in one dimension under the non-zero mass condition. If the corresponding Riemann problem for the compressible Euler system admits a contact discontinuity solution, it is shown that the contact wave is nonlinearly stable, while the strength of the contact discontinuity and the initial perturbation are suitably small. Especially, we obtain the decay rate of contact waves by using anti-derivative methods and elaborated energy estimates.

On Euler systems for the multiplicative group over general number fields

On Euler systems for the multiplicative group over general number fields

On the Lagrangian description and uniqueness for the one-dimensional pressureless Euler system

On the Lagrangian description and uniqueness for the one-dimensional pressureless Euler system

Radially symmetric non-isentropic Euler flows: Continuous blowup with positive pressure

We establish the existence of radial self-similar Euler flows in which a continuous incoming wave generates a blowup of primary (undifferentiated) flow variables. A key point is that the solutions have a strictly positive pressure field, in contrast to Guderley's classic construction of converging shock waves. In Guderley's solutions, a converging shock invades a quiescent region at zero pressure (due to vanishing temperature), and the velocity and pressure in its immediate wake become unbounded at the time of collapse. It is reasonable that the lack of upstream counter-pressure is conducive to large speeds, with concomitant large amplitudes. Based on Guderley's original solutions, it is therefore unclear if it is the zero-pressure region that is responsible for blowup. The same applies to self-similar Euler flows describing radial cavity flow. Our results demonstrate that the geometric mechanism of wave focusing is sufficiently strong on its own to drive unbounded growth. We propagate the solution beyond blowup and observe numerically that there are two distinct possibilities depending on the incoming flow: either an expanding spherical shock wave is generated, or the flow propagates in a continuous manner. Focusing on the former case, we show that the resulting flows define global admissible weak solutions to the full, multi-d compressible Euler system. These solutions have the unusual property that the flow is isentropic in each of the two regions separated by the shock.

Asymptotic stability of a composite wave to the one-dimensional compressible Navier-Stokes equations for a reacting mixture

This paper is concerned with the large time behavior of solutions for the Cauchy problem to the compressible Navier-Stokes equations for a reacting mixture with zero viscosity in one dimension. If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves and contact discontinuity, it is shown that the composition of two rarefaction waves with a viscous contact wave is asymptotically stable, while the strength of the composite wave and the initial perturbation are suitably small.

A MOOD-like compact high order finite volume scheme with adaptive mesh refinement

In this paper, a novel Finite Volume (FV) scheme for obtaining high order approximations of solutions of multi-dimensional hyperbolic systems of conservation laws within an Adaptive Mesh Refinement framework is proposed. It is based on a point-wise polynomial reconstruction that avoids the recalculation of reconstruction stencils and matrices whenever a mesh is refined or coarsened. It also couples both the limiting of the FV scheme and the refinement procedure, taking advantage of the Multi-dimensional Optimal Order Detection (MOOD) detection criteria. The resulting computational procedure is employed to simulate test cases of increasing difficulty using two models of Partial Differential Equations: the Euler system and the radiative M1 model, thus demonstrating its efficiency.