scholarly journals A Godunov-Type Solver for the Numerical Approximation of Gravitational Flows

2014 ◽  
Vol 15 (1) ◽  
pp. 46-75 ◽  
Author(s):  
J. Vides ◽  
B. Braconnier ◽  
E. Audit ◽  
C. Berthon ◽  
B. Nkonga
Keyword(s):  
Numerical Method ◽  
Euler Equations ◽  
Numerical Experiments ◽  
Numerical Approximation ◽  
Source Term ◽  
Poisson Model ◽  
Riemann Solver ◽  
Approximate Riemann Solver ◽  
Relaxation Scheme ◽  
Astrophysical Flows

AbstractWe present a new numerical method to approximate the solutions of an Euler-Poisson model, which is inherent to astrophysical flows where gravity plays an important role. We propose a discretization of gravity which ensures adequate coupling of the Poisson and Euler equations, paying particular attention to the gravity source term involved in the latter equations. In order to approximate this source term, its discretization is introduced into the approximate Riemann solver used for the Euler equations. A relaxation scheme is involved and its robustness is established. The method has been implemented in the software HERACLES [29] and several numerical experiments involving gravitational flows for astrophysics highlight the scheme.

A 3D Approximate Riemann Solver for the Euler Equations Using Flux Splitting Schemes With a Robust Multigrid

2016 ◽  
Author(s):  
Hong-Sik Im
Keyword(s):  
Euler Equations ◽  
Riemann Solver ◽  
Riemann Solvers ◽  
Approximate Riemann Solver ◽  
Time Stepping ◽  
Flux Vector Splitting ◽  
Time Marching ◽  
Convergence To Steady State ◽  
Flux Difference ◽  
Robust Multigrid

An explicit 3D approximate Riemann solver for the Euler equations is proposed using the famous shock capturing schemes with a simple cell vertex based multigrid method. A multistage Runge-Kutta time marching scheme with a local time stepping is used to achieve fast convergence to steady state. A Roe’s flux difference splitting, AUSM+, Van Leer and Steger-Warming’s flux vector splitting are implemented as base Riemann solvers with a third order flux reconstruction. It is shown that the proposed Riemann solvers accurately capture the shocks as well as reduce CPU time significantly with new multigrid.

Anh-r-Adaptive Approximate Riemann Solver for the Euler Equations in Two Dimensions

1993 ◽  
Vol 14 (1) ◽  
pp. 185-217 ◽  
Author(s):  
Michael G. Edwards ◽  
J. Tinsley Oden ◽  
Leszek Demkowicz
Keyword(s):  
Euler Equations ◽  
Two Dimensions ◽  
Riemann Solver ◽  
Approximate Riemann Solver

scholarly journals An Approximate Riemann Solver for Euler Equations

10.5772/39028 ◽  
2012 ◽  
Author(s):  
Oscar Falcinelli ◽  
Sergio Elaskar ◽  
Jos Tamagno ◽  
Jorge Colman
Keyword(s):  
Euler Equations ◽  
Riemann Solver ◽  
Approximate Riemann Solver

scholarly journals RELAXATION OF FLUID SYSTEMS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250014 ◽  
Author(s):  
FRÉDÉRIC COQUEL ◽  
EDWIGE GODLEWSKI ◽  
NICOLAS SEGUIN
Keyword(s):  
Numerical Method ◽  
Weak Solutions ◽  
Equilibrium Model ◽  
Numerical Approximation ◽  
Natural Extension ◽  
Fluid Models ◽  
Relaxation System ◽  
Fluid Systems ◽  
Relaxation Procedure ◽  
Entropy Inequalities

We propose a relaxation framework for general fluid models which can be understood as a natural extension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The numerical method is particularly simple in the case of a fully degenerate relaxation system for which the solution of the Riemann problem is explicit. Indeed, the Godunov solver for the homogeneous relaxation system results in an HLLC-type solver for the equilibrium model. Discrete entropy inequalities are established under a natural Gibbs principle.

The development of a Riemann solver for the steady supersonic Euler equations

1994 ◽  
Vol 98 (979) ◽  
pp. 325-339 ◽  
Author(s):  
E. F. Toro ◽  
A. Chakraborty
Keyword(s):  
Euler Equations ◽  
Weighted Average ◽  
Godunov Method ◽  
Riemann Solver ◽  
Flux Method ◽  
First Order ◽  
Enhanced Resolution ◽  
Average Flux ◽  
Exact Riemann Solver ◽  
Order Weighted Average

Abstract An improved version (HLLC) of the Harten, Lax, van Leer Riemann solver (HLL) for the steady supersonic Euler equations is presented. Unlike the HLL, the HLLC version admits the presence of the slip line in the structure of the solution. This leads to enhanced resolution of computed slip lines by Godunov type methods. We assess the HLLC solver in the context of the first order Godunov method and the second order weighted average flux method (WAF). It is shown that the improvement embodied in the HLLC solver over the HLL solver is virtually equivalent to incorporating the exact Riemann solver.

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

scholarly journals Approximate Riemann solver for hypervelocity flows

AIAA Journal ◽  
1992 ◽  
Vol 30 (10) ◽  
pp. 2558-2561 ◽  
Author(s):  
P. A. Jacobs
Keyword(s):  
Riemann Solver ◽  
Approximate Riemann Solver ◽  
Hypervelocity Flows

scholarly journals Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner

2018 ◽  
Vol 52 (4) ◽  
pp. 1285-1313 ◽  
Author(s):  
Lucas Chesnel ◽  
Xavier Claeys ◽  
Sergei A. Nazarov
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Recent Work ◽  
Present Article ◽  
Error Estimates ◽  
Numerical Experiments ◽  
Source Term ◽  
Oscillatory Behaviour ◽  
Time Harmonic ◽  
Rounded Corner

We investigate the eigenvalue problem −div(σ∇u) = λu (P) in a 2D domain Ω divided into two regions Ω±. We are interested in situations where σ takes positive values on Ω+ and negative ones on Ω−. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [L. Chesnel, X. Claeys and S.A. Nazarov, Asymp. Anal. 88 (2014) 43–74], we highlighted an unusual instability phenomenon for the source term problem associated with (P): for certain configurations, when the interface between the subdomains Ω± presents a rounded corner, the solution may depend critically on the value of the rounding parameter. In the present article, we explain this property studying the eigenvalue problem (P). We provide an asymptotic expansion of the eigenvalues and prove error estimates. We establish an oscillatory behaviour of the eigenvalues as the rounding parameter of the corner tends to zero. We end the paper illustrating this phenomenon with numerical experiments.

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