CONDIF: A MODIFIED CENTRAL-DIFFERENCE SCHEME WITH UNCONDITIONAL STABILITY AND VERY LOW NUMERICAL DIFFUSION

1986 ◽  
Author(s):  
Akshai K. Runchal
Keyword(s):  
Difference Scheme ◽  
Unconditional Stability ◽  
Central Difference ◽  
Numerical Diffusion ◽  
Central Difference Scheme

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

Monotonic Convergence Property of Turbulent Flow Solution With Central Difference and QUICK Schemes

1999 ◽  
Vol 121 (2) ◽  
pp. 351-358 ◽  
Author(s):  
Toshiyuki Hayase
Keyword(s):  
Turbulent Flow ◽  
Difference Scheme ◽  
Numerical Solutions ◽  
Richardson Extrapolation ◽  
Grid Refinement ◽  
Central Difference ◽  
Central Difference Scheme ◽  
Quick Scheme ◽  
Discretization Schemes ◽  
Monotonic Convergence

Monotonic convergence of numerical solutions with the computational grid refinement is an essential requirement in estimating the grid-dependent uncertainty of computational fluid dynamics. If the convergence is not monotonic, the solution could be erroneously regarded as convergent at the local extremum with respect to some measure of the error. On the other hand, if the convergence is exactly monotonic, estimation methods such as Richardson extrapolation properly evaluate the uncertainty of numerical solutions. This paper deals with the characterization of numerical schemes based on the property of the monotonic convergence of numerical solutions. Two typical discretization schemes of convective terms were considered; the second-order central difference scheme and the third-order Leonard’s QUICK scheme. A fully developed turbulent flow through a square duct was calculated via a SIMPLER based finite volume method without a turbulence model. The convergence of the numerical solution with the grid refinement was investigated for the mean flow property as well as fluctuations. The comparison of convergence process between the discretization schemes has revealed that the QUICK scheme results in preferable monotonic convergence, while the second-order central difference scheme undergoes non-monotonic convergence. The latter possibly misleads the determination of convergence with the grid refinement, or causes trouble in applying the Richardson extrapolation procedure to estimate the numerical uncertainty.

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