scholarly journals CORRECTION TO THE PAPER: AN ENERGY DISSIPATIVE SPATIAL DISCRETIZATION FOR THE REGULARIZED COMPRESSIBLE NAVIER-STOKES-CAHN-HILLIARD SYSTEM OF EQUATIONS (IN MATH. MODEL. ANAL., 25(1): 110–129, HTTPS://DOI.ORG/10.3846/MMA.2020.10577)

2021 ◽  
Vol 26 (2) ◽  
pp. 337-338
Author(s):  
Vladislav Balashov ◽  
Alexander Zlotnik
Keyword(s):  
Finite Difference ◽  
Navier Stokes ◽  
System Of Equations ◽  
Spatial Discretization ◽  
Equilibrium Solutions ◽  
Math Model

We correct the proof of Theorem 2 in the mentioned paper concerning finite-difference equilibrium solutions.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

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