scholarly journals A SECOND-ORDER GODUNOV METHOD FOR MULTI-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMICS

2011 ◽  
Vol 193 (1) ◽  
pp. 6 ◽  
Author(s):  
Kris Beckwith ◽  
James M. Stone
Keyword(s):  
Second Order ◽  
Godunov Method ◽  
Relativistic Magnetohydrodynamics

Application of the Godunov method and its second-order extension to cascade flow modeling

AIAA Journal ◽  
1984 ◽  
Vol 22 (11) ◽  
pp. 1609-1615 ◽  
Author(s):  
Shmuel Eidelman ◽  
Phillip Colella ◽  
Raymond P. Shreeve
Keyword(s):  
Second Order ◽  
Godunov Method ◽  
Flow Modeling ◽  
Cascade Flow ◽  
Order Extension

scholarly journals Numerical Simulations of Extragalactic Jets in an Inhomogeneous Environment

1996 ◽  
Vol 175 ◽  
pp. 467-468
Author(s):  
Steve Higgins ◽  
TIM O'BRIEN ◽  
James Dunlop
Keyword(s):  
Numerical Simulations ◽  
Three Dimensional ◽  
Second Order ◽  
Godunov Method ◽  
Radio Sources ◽  
Cartesian Coordinates ◽  
Extragalactic Radio Sources ◽  
Extragalactic Jets ◽  
Hydrodynamic Code

We have simulated the passage of an extragalactic jet through a medium containing an ensemble of cool, dense clouds. The hydrodynamic code uses the second-order Godunov method of Falle (Falle 1991, van Leer 1979) in three-dimensional, cartesian coordinates. We have estimated the synchrotron emissivity and used this to produce synthetic radio maps. The results are reminiscent of structures seen in many extragalactic radio sources.

Schemes of the second order accuracy for computing the dynamics of disturbances in an elastic body

2017 ◽  
Vol 12 (1) ◽  
pp. 44-50 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Analytic Solutions ◽  
Second Order ◽  
The Body ◽  
Godunov Method ◽  
Tvd Scheme ◽  
Order Accuracy ◽  
Linear Waves ◽  
Approximation Errors ◽  
The Impact

The efficiency of the second-order accurate UNO- and TVD-modifications of the Godunov method is compared using a number of problems on the propagation of linear waves in an elastic body, their interaction with each other and with the surface of the body. In particular, one-dimensional problems having analytic solutions and a two-dimensional problem of the dynamics of a body in the vicinity of the impact domain on its free surface are considered. It is shown that if in the problems there are well-marked extrema or short waves, then the UNO-scheme is more effective, since in such cases decrease in the accuracy of the TVD-scheme becomes apparent due to strictly satisfying the TVD condition. Because of approximately satisfying the TVD condition, the UNO-scheme can lead to the appearance of oscillations of numerical nature at the level of approximation errors. However, this does not reduce the efficiency of the UNO scheme since the amplitude of those oscillations decreases with refinement of the grid.

scholarly journals A Comparison of Modern Hyperbolic Methods for Semiconductor Device Simulation: NTK Central Scheme Vs. CLAWPACK

VLSI Design ◽  
2002 ◽  
Vol 15 (4) ◽  
pp. 721-728
Author(s):  
Carl L. Gardner ◽  
Anne Gelb ◽  
Justin Hernandez
Keyword(s):  
Hydrodynamic Model ◽  
Software Package ◽  
Semiconductor Device ◽  
Splitting Method ◽  
Device Simulation ◽  
Second Order ◽  
Godunov Method ◽  
Source Terms ◽  
Central Scheme ◽  
Classical Hydrodynamic

Two modern hyperbolic methods—a second-order Godunov method in the software package CLAWPACK and the second-order Nessyahu–Tadmor–Kurganov (NTK) central scheme—are compared for simulating an electron shock wave in the classical hydrodynamic model for semiconductor devices.The NTK central scheme, which does not employ Riemann problem solutions, is described in detail. Special attention is paid in both methods to handling the source terms in the hydrodynamic model. CLAWPACK incorporates the source terms by a splitting method, while our version of the NTK scheme is unsplit.

scholarly journals Efficient approach toward the application of the Godunov method to hydraulic transients

2020 ◽  
Vol 22 (5) ◽  
pp. 1370-1390 ◽  
Author(s):  
Susovan Pal ◽  
Prashanth Reddy Hanmaiahgari ◽  
Martin F. Lambert
Keyword(s):  
Finite Volume ◽  
Water Hammer ◽  
Friction Model ◽  
Second Order ◽  
Godunov Method ◽  
Computational Time ◽  
Godunov Scheme ◽  
Riemann Solvers ◽  
First Order ◽  
Volume Method

Abstract The proposed study investigated the applicability of the finite volume method (FVM) based on the Godunov scheme to transient water hammer with shock front simulation, in which intermediate fluxes were computed using either first-order or second-order Riemann solvers. Finite volume (FV) schemes are known to conserve mass and momentum and produce the efficient and accurate realization of shock waves. The second-order solution of the Godunov scheme requires an efficient slope or a flux limiter for error minimization and time optimization. The study examined a range of limiters and found that the MINMOD limiter is the best for modeling water hammer in terms of computational time and accuracy. The first- and second-order FVMs were compared with the method of characteristics (MOCs) and experimental water hammer measurements available in the literature. Both the FV methods accurately predicted the numerical and experimental results. Parallelization of the second-order FVM reduced the computational time similar to that of first-order. Thus, the study presented a faster and more accurate FVM which is comparable to that of MOC in terms of computational time and precision, therefore it is a good substitute for the MOC. The proposed study also investigated the implementation of a more complex convolution-based unsteady friction model in the FVM to capture real pressure dissipation. The comparison with experimental data proved that the first-order FV scheme with the convolution integral method is highly accurate for computing unsteady friction for sudden valve closures.

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