scholarly journals ON THE USE OF THE CENTRAL DIFFERENCE SCHEME FOR SOLVING THE PROBLEM OF GAS DYNAMICS

2021 ◽  
pp. 17-22
Author(s):  
I.I. Potapov ◽  
◽  
P.S. Timosh ◽  
Keyword(s):  
Difference Scheme ◽  
Gas Dynamics ◽  
Central Difference ◽  
Central Difference Scheme ◽  
The Stability

The paper proposes a method for solving the problem of gas dynamics, implemented on the basis of a central difference scheme, the stability of which is achieved by performing a correction of the calcu-lated flows. It is shown that when solving the problem of discontinuity decay, the proposed method is stable, comparable in accuracy with the McCormack and Lax – Wendroff methods and surpasses them in performance.

The role and application of entropy terms for acoustic wave modeling by the finite‐difference method

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1457-1465 ◽  
Author(s):  
M. A. Dablain
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Acoustic Wave Propagation ◽  
Central Difference ◽  
Central Difference Scheme ◽  
One Dimensional ◽  
The Finite Difference Method

The significance of entropy‐like terms is examined within the context of the finite‐difference modeling of acoustic wave propagation. The numerical implications of dissipative mechanisms are tested for performance within two very distinct differencing algorithms. The two schemes which are reviewed with and without dissipation are (1) the standard central‐difference scheme, and (2) the Lax‐Wendroff two‐step scheme. Numerical results are presented comparing the short‐wavelength response of these schemes. In order to achieve this response, the linearized version of an exploding one‐dimensional source is used.

scholarly journals On the determination of the dissipation rate of turbulence kinetic energy

2021 ◽  
Vol 62 (7) ◽  
Author(s):  
James M. Lewis ◽  
Timothy W. Koster ◽  
John C. LaRue
Keyword(s):  
Kinetic Energy ◽  
Difference Scheme ◽  
Dissipation Rate ◽  
Hot Wire ◽  
Central Difference ◽  
Time Resolved ◽  
Central Difference Scheme ◽  
Derivative Spectra ◽  
Velocity Derivative ◽  
Velocity Spectra

Abstract The paper presents a comparison of the dissipation rate obtained from numerical differentiation of the time-resolved velocity, analog differentiation of the hot-wire signal, integration of the velocity derivative spectra obtained from the velocity spectra, and the application of a power decay law. Hot-wire measurements downstream of an active-grid provide the time-resolved velocity with a Taylor Reynolds number in the range of 200–470, turbulence intensities in the range of 5.8–11%, and nominal mean velocities of 4, 6, and 8 m s$$^{-1}$$ - 1 . The dissipation rate calculated using a ninth-order central-difference scheme differs at most by $${\pm }$$ ±  4% from the value obtained by analog differentiation. For comparison, a 23rd-order central-difference scheme offers negligible (0.02%) difference relative to the ninth-order scheme. Correction for an apparent uncertainty in the calibration of the analog differentiator reduces the difference to $${\pm }$$ ±  2.5%. In contrast, integration of the velocity derivative spectra obtained from the velocity spectra leads to a dissipation rate 14–45% larger than the corresponding values obtained using analog differentiation. Results obtained from the application of a power decay law of turbulence kinetic energy with a nonzero virtual origin to determine the dissipation rate deviate by 1.7%, 1.6%, and 3.6% relative to the corresponding values obtained from the analog differentiator based on the ensemble average of downstream locations with a $${\pm }$$ ± 5.6% scatter about the ensemble average. Graphic abstract

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