Splitting Algorithms for Numerical Solution of Navier-Stokes Equations in Fluid Dynamics Problems

2021 ◽  
Vol 62 (3) ◽  
pp. 48-59
Author(s):  
V. M. Kovenya
Keyword(s):  
Fluid Dynamics ◽  
Numerical Solution ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Splitting Algorithms ◽  
Dynamics Problems

Splitting algorithms for numerical solution of Euler and Navier–Stokes problems

2014 ◽  
Vol 29 (6) ◽  
Author(s):  
Victor M. Kovenya
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Stability Margin ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Grid Node ◽  
Navier Stokes Equations ◽  
Splitting Algorithms ◽  
Splitting Technique ◽  
Stokes Problems

AbstractAn optimal splitting technique is proposed for numerical solution of the Euler and Navier-Stokes equations for a compressible heat-conducting gas. This technique is common for original equations in the divergent and nondivergent form. Based on this splitting, a class of economical (in the number of operations per a grid node) difference schemes is proposed so that those schemes are implemented on fractional steps by the scalar sweep methods and have a large stability margin, but have a lesser number of sweep steps in their implementation.

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Development of SIMPLE-Like Algorithms for Incompressible Navier-Stokes Equations in Liquid Processing of Materials

2012 ◽  
Vol 184-185 ◽  
pp. 944-948 ◽  
Author(s):  
Hai Jun Gong ◽  
Yang Liu ◽  
Xue Yi Fan ◽  
Da Ming Xu
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Simple Algorithm ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Numerical Accuracy ◽  
Simple Scheme ◽  
Navier Stokes Equations ◽  
Computational Fluid Dynamics Cfd

For a clear and comprehensive opinion on segregated SIMPLE algorithm in the area of computational fluid dynamics (CFD) during liquid processing of materials, the most significant developments on the SIMPLE algorithm and its variants are briefly reviewed. Subsequently, some important advances during last 30 years serving as increasing numerical accuracy, enhancing robustness and improving efficiency for Navier–Stokes (N-S) equations of incompressible fluid flow are summarized. And then a so-called Direct-SIMPLE scheme proposed by the authors of present paper introduced, which is different from SIMPLE-like schemes, no iterative computations are needed to achieve the final pressure and velocity corrections. Based on the facts cited in present paper, it conclude that the SIMPLE algorithm and its variants will continue to evolve aimed at convergence and accuracy of solution by improving and combining various methods with different grid techniques, and all the algorithms mentioned above will enjoy widespread use in the future.

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