scholarly journals Asymptotic preserving discretization of a Jin–Xin model with implicit equilibrium manifold on a bounded domain

2019 ◽  
Vol 40 (1) ◽  
pp. 530-562
Author(s):  
Nicolas Seguin ◽  
Magali Tournus
Keyword(s):  
Linear System ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Numerical Scheme ◽  
Asymptotic Limit ◽  
Implicit Function ◽  
Asymptotic Preserving ◽  
Equilibrium Manifold

Abstract In this paper, we design and analyze a numerical scheme that approximates a Jin–Xin linear system with implicit equilibrium on a bounded domain. This scheme relaxes toward the asymptotic limit of the linear system. The main properties of the limiting scheme are that it does not require to invert the implicit function defining the manifold and that it provides an accurate discretization of the boundary conditions.

Research on Dynamic Simulation of AUV Launching a Towed Navigation Buoyage

2013 ◽  
Vol 433-435 ◽  
pp. 1170-1174
Author(s):  
Guang Pan ◽  
Zhi Dong Yang ◽  
Xiao Xu Du
Keyword(s):  
Angular Momentum ◽  
Boundary Conditions ◽  
Dynamic Simulation ◽  
Numerical Scheme ◽  
Mathematic Model ◽  
Dynamic Equations ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Towed Cable ◽  
Undersea Vehicle

A mathematic model was established to simulate the process of AUV (autonomous undersea vehicle) launching a towed buoyage. Based on the lumped mass method and moment theorem and angular momentum theorem, dynamic equations of the cable and the buoyage were developed, respectively. Then the boundary conditions and the numerical scheme to deal with the cable with non-fixed length were presented. Moreover, the process of AUV launching a towed cable was simulated. By using the model, the results show the trajectory of buoyage and shape of towed cable can be well predicted.

Multiple solutions for a non-homogeneous elliptic equation at the critical exponent

2004 ◽  
Vol 134 (1) ◽  
pp. 69-87 ◽  
Author(s):  
Mónica Clapp ◽  
Manuel Del Pino ◽  
Monica Musso
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Critical Exponent ◽  
Bounded Domain ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Sign Changing Solutions ◽  
Homogeneous Elliptic Equation

We consider the equation−Δu = |u|4/(N−2)u + εf(x) under zero Dirichlet boundary conditions in a bounded domain Ω in RN exhibiting certain symmetries, with f ≥ 0, f ≠ 0. In particular, we find that the number of sign-changing solutions goes to infinity for radially symmetric f, as ε → 0 if Ω is a ball. The same is true for the number of negative solutions if Ω is an annulus and the support of f is compact in Ω.

An Admissible Asymptotic-Preserving Numerical Scheme for the Electronic M1 Model in the Diffusive Limit

2018 ◽  
Vol 24 (5) ◽  
Author(s):  
Sebastien Guisset ◽  
Stephane Brull ◽  
Bruno Dubroca ◽  
Rodolphe Turpault
Keyword(s):  
Numerical Scheme ◽  
Asymptotic Preserving ◽  
Diffusive Limit

Analysis of an elliptic system with infinitely many solutions

2017 ◽  
Vol 6 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Carmen Cortázar ◽  
Manuel Elgueta ◽  
Jorge García-Melián
Keyword(s):  
Boundary Conditions ◽  
Elliptic System ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Infinitely Many Solutions ◽  
Smooth Bounded Domain ◽  
Content Type ◽  
Outward Unit ◽  
Unit Normal

AbstractWe consider the elliptic system ${\Delta u\hskip-0.284528pt=\hskip-0.284528ptu^{p}v^{q}}$, ${\Delta v\hskip-0.284528pt=\hskip-0.284528ptu^{r}v^{s}}$ in Ω with the boundary conditions ${{\partial u/\partial\eta}=\lambda u}$, ${{\partial v/\partial\eta}=\mu v}$ on ${\partial\Omega}$, where Ω is a smooth bounded domain of ${\mathbb{R}^{N}}$, ${p,s>1}$, ${q,r>0}$, ${\lambda,\mu>0}$ and η stands for the outward unit normal. Assuming the “criticality” hypothesis ${(p-1)(s-1)=qr}$, we completely analyze the values of ${\lambda,\mu}$ for which there exist positive solutions and give a detailed description of the set of solutions.

scholarly journals Four Spacetime Dimensional Simulation of Rheological Waves in Solids and the Merits of Thermodynamics

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1376
Author(s):  
Áron Pozsár ◽  
Mátyás Szücs ◽  
Róbert Kovács ◽  
Tamás Fülöp
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Boundary Conditions ◽  
Numerical Scheme ◽  
Dispersion Error ◽  
Finite Element Software ◽  
Dimensional Simulation

The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions and in the aspect of the virtues of a thermodynamical approach. Regarding the scheme, the arrangement of which quantity is represented where in discretized spacetime, including the question of appropriately realizing the boundary conditions, is nontrivial. In parallel, placing the problem in the thermodynamical framework proves to be beneficial in regards to monitoring and controlling numerical artefacts—instability, dissipation error, and dispersion error. This, in addition to the observed preciseness, speed, and resource-friendliness, makes the thermodynamically extended symplectic approach that is presented here advantageous above commercial finite element software solutions.

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