A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow

1986 ◽  
Vol 7 (3) ◽  
pp. 870-891 ◽  
Author(s):  
J. van Kan
Keyword(s):  
Incompressible Flow ◽  
Second Order ◽  
Pressure Correction ◽  
Viscous Incompressible Flow ◽  
Correction Scheme

scholarly journals Stability of a Crank-Nicolson pressure correction scheme based on staggered discretizations

2013 ◽  
Vol 74 (1) ◽  
pp. 34-58
Author(s):  
F. Boyer ◽  
F. Dardalhon ◽  
C. Lapuerta ◽  
J.-C. Latché
Keyword(s):  
Pressure Correction ◽  
Correction Scheme ◽  
Crank Nicolson

Time dispersion correction for arbitrarily even-order Lax-Wendroff methods and the application on full waveform inversion

Geophysics ◽  
2021 ◽  
pp. 1-89
Author(s):  
Zhiming Ren ◽  
Qianzong Bao ◽  
Bingluo Gu
Keyword(s):  
Waveform Inversion ◽  
Second Order ◽  
High Order ◽  
Full Waveform Inversion ◽  
Dispersion Correction ◽  
Equal Time ◽  
Full Waveform ◽  
Time Dispersion ◽  
Correction Scheme ◽  
Even Order

A second-order accurate finite-difference (FD) approximation is commonly used to approximate the second-order time derivative of wave equation. The second-order accurate FD scheme may introduce time dispersion in wavefield extrapolation. Lax-Wendroff methods can suppress such dispersion by replacing the high-order time FD error-terms with space FD error correcting terms. However, the time dispersion cannot be completely eliminated and the computation cost dramatically increases with increasing order of (temporal) accuracy. To mitigate the problem, we extend the existing time dispersion correction scheme for second- or fourth-order Lax-Wendroff method to a scheme for arbitrary even-order methods, which uses the forward and inverse time dispersion transform (FTDT and ITDT) to add and remove the time dispersion from synthetic data. We test the correction scheme using a homogeneous model and the Sigsbee2A model. Modeling examples suggest that the use of derived FTDT and ITDT pairs on high-order Lax-Wendroff methods can effectively remove time dispersion errors from high-frequency waves while using longer time steps than allowed in low-order Lax-Wendroff methods. We investigate the influence of the time dispersion on full waveform inversion (FWI) and show an anti-dispersion workflow. We apply the FTDT to source terms and recorded traces before inversion, resulting in that the source and adjoint wavefields contain equal time dispersion from source-side wave propagation, and the modeled and observed traces accumulate equal time dispersion from source- and receiver-side wave propagation. Inversion results reveal that the anti-dispersion workflow is capable of increasing the accuracy of FWI for arbitrary even-order Lax-Wendroff methods. Additionally, the high-order method can obtain better inversion results compared to the second-order method with the same anti-dispersion workflow.

On Analysis of Stationary Viscous Incompressible Flow Through a Radial Blade Machine

2010 ◽  
Author(s):  
Tomáš Neustupa ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Incompressible Flow ◽  
Viscous Incompressible Flow ◽  
Flow Through

scholarly journals An adjoint-based pressure correction scheme

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 861-862
Author(s):  
Julius Reiss
Keyword(s):  
Pressure Correction ◽  
Correction Scheme
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