Nonoscillatory Central Difference and Artificial Viscosity Schemes for Relativistic Hydrodynamics

2003 ◽  
Vol 144 (2) ◽  
pp. 243-257 ◽  
Author(s):  
Peter Anninos ◽  
P. Chris Fragile
Keyword(s):  
Artificial Viscosity ◽  
Relativistic Hydrodynamics ◽  
Central Difference

Influence of the Artificial Dissipation Model on the Propagation of Acoustic and Entropy Waves

2000 ◽  
Author(s):  
Roque Corral ◽  
Manuel Antonio Burgos ◽  
Antonio García
Keyword(s):  
Theoretical Analysis ◽  
Acoustic Waves ◽  
Numerical Experiments ◽  
Artificial Viscosity ◽  
Central Difference ◽  
Subsonic Flows ◽  
Artificial Dissipation ◽  
Difference Type ◽  
Dissipation Model ◽  
Dissipative Terms

The aim of this work is to show that the form of the artificial dissipation terms used in central-difference-type schemes to stabilise the solution of the unsteady Euler equations may play a crucial role on the propagation of entropy, vorticity and acoustic waves. It will be demonstrated by means of numerical experiments and theoretical analysis that the scalar formulation of the artificial viscosity prevents the correct propagation of entropy and vorticity waves for moderate low Mach numbers and that the upstream propagation of acoustic waves degrades significantly for high subsonic flows. It will be proved that if the scaling of the dissipative terms takes into account the fact that the entropy and acoustic waves may propagate at quite different velocities, the accuracy of the scheme is greatly improved. Actually it will be demonstrated that there exists a class of problems for which the standard scheme is unable to produce equivalent solutions to the ones obtained by the matricial model, without a large penalty in the number of points.

Finite Difference Method on Non-Uniform Meshes for Time Fractional Diffusion Problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Haili Qiao ◽  
Aijie Cheng
Keyword(s):  
Theoretical Analysis ◽  
Fractional Derivative ◽  
Time Discretization ◽  
Summation Formula ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Initial Moment ◽  
Central Difference ◽  
Ideal Convergence ◽  
Derivative Term

AbstractIn this paper, we consider the time fractional diffusion equation with Caputo fractional derivative. Due to the singularity of the solution at the initial moment, it is difficult to achieve an ideal convergence rate when the time discretization is performed on uniform meshes. Therefore, in order to improve the convergence order, the Caputo time fractional derivative term is discretized by the {L2-1_{\sigma}} format on non-uniform meshes, with {\sigma=1-\frac{\alpha}{2}}, while the spatial derivative term is approximated by the classical central difference scheme on uniform meshes. According to the summation formula of positive integer k power, and considering {k=3,4,5}, we propose three non-uniform meshes for time discretization. Through theoretical analysis, different time convergence orders {O(N^{-\min\{k\alpha,2\}})} can be obtained, where N denotes the number of time splits. Finally, the theoretical analysis is verified by several numerical examples.

scholarly journals Frequency-Dependent FDTD Algorithm Using Newmark’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bing Wei ◽  
Le Cao ◽  
Fei Wang ◽  
Qian Yang
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Field Intensity ◽  
Time Domain ◽  
Difference Method ◽  
Electric Field Intensity ◽  
Polarization Vector ◽  
Solution Stability ◽  
Central Difference ◽  
Central Difference Method

According to the characteristics of the polarizability in frequency domain of three common models of dispersive media, the relation between the polarization vector and electric field intensity is converted into a time domain differential equation of second order with the polarization vector by using the conversion from frequency to time domain. Newmarkβγdifference method is employed to solve this equation. The electric field intensity to polarizability recursion is derived, and the electric flux to electric field intensity recursion is obtained by constitutive relation. Then FDTD iterative computation in time domain of electric and magnetic field components in dispersive medium is completed. By analyzing the solution stability of the above differential equation using central difference method, it is proved that this method has more advantages in the selection of time step. Theoretical analyses and numerical results demonstrate that this method is a general algorithm and it has advantages of higher accuracy and stability over the algorithms based on central difference method.

Impact of Different Film-Cooling Modes at Trailing Edge on the Aerodynamic Performance of Heavy Duty Gas Turbine Cascade

2011 ◽  
Vol 84-85 ◽  
pp. 259-263
Author(s):  
Xun Liu ◽  
Song Tao Wang ◽  
Xun Zhou ◽  
Guo Tai Feng
Keyword(s):  
Gas Turbine ◽  
Film Cooling ◽  
Large Mass ◽  
Turbine Cascade ◽  
Heavy Duty ◽  
Trailing Edge ◽  
Central Difference ◽  
Adiabatic Effectiveness ◽  
Heavy Duty Gas Turbine ◽  
The Impact

In this paper, the trailing edge film cooling flow field of a heavy duty gas turbine cascade has been studied by central difference scheme and multi-block grid technique. The research is based on the three-dimensional N-S equation solver. By way of analysis of the temperature field, the distribution of profile pressure, and the distribution of film-cooling adiabatic effectiveness in the region of trailing edge with different cool air injection mass and different angles, it is found that the impact on the film-cooling adiabatic effectiveness is slightly by changing the injection mass. The distribution of profile pressure dropped intensely at the pressure side near the injection holes line with the large mass cooling air. The cooling effect is good in the region of trailing edge while the injection air is along the direction of stream.

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