Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier-Stokes equations

DOI10.1016/j.amc.2017.06.037zbMath1426.76449OpenAlexW2688999378MaRDI QIDQ1740113

Roberto La Scala, Pierluigi Amodio, Yu. A. Blinkov, Vladimir P. Gerdt

Publication date: 29 April 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2017.06.037

zbMATH Keywords

finite difference methodGröbner basesstrong consistency2D Navier-Stokes equationsdifference algebra

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite difference methods applied to problems in fluid mechanics (76M20) Navier-Stokes equations (35Q30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Difference algebra (12H10) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (4)

A strongly-consistent difference scheme for 3D nonlinear Navier-Stokes equations ⋮ Investigation of difference schemes for two-dimensional Navier-Stokes equations by using computer algebra algorithms ⋮ On the consistency analysis of finite difference approximations ⋮ Algebraic construction of a strongly consistent, permutationally symmetric and conservative difference scheme for 3D steady Stokes flow

Uses Software

• DifferentialThomas

Cites Work

• Algorithmic Thomas decomposition of algebraic and differential systems
• Formal algorithmic elimination for PDEs
• Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals
• Involution. The formal theory of differential equations and its applications in computer algebra
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• A discrete vector calculus in tensor grids
• Difference algebra
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• Involution and Difference Schemes for the Navier–Stokes Equations
• On pressure boundary conditions for the incompressible Navier-Stokes equations
• Numerical Solution of Partial Differential Equations
• On Consistency of Finite Difference Approximations to the Navier-Stokes Equations
• Gröbner bases and gradings for partial difference ideals
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