# A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations

@article{Blinkov2018ASC, title={A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations}, author={Y. Blinkov and V. Gerdt and D. Lyakhov and D. Michels}, journal={ArXiv}, year={2018}, volume={abs/1807.00328} }

We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorporated into the scheme. Our approach suggested by the first two authors is based on a combination of the finite volume method, difference elimination, and numerical integration. We make use of the techniques of the differential and difference Janet/Grobner bases. In order to prove strong consistency of the generated… Expand

#### References

SHOWING 1-10 OF 22 REFERENCES

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

- Mathematics, Computer Science
- Appl. Math. Comput.
- 2017

In this paper, we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional Navier–Stokes equations… Expand

Involution and Difference Schemes for the Navier-Stokes Equations

- Mathematics, Computer Science
- CASC
- 2009

By exploiting arbitrariness in the numerical integration approximation the Navier---Stokes equations are considered and two finite-difference schemes are derived that are similar to the classical scheme by Harlow and Welch. Expand

On Consistency of Finite Difference Approximations to the Navier-Stokes Equations

- Mathematics, Computer Science
- CASC
- 2013

It is proved that only one of these approximations is strongly consistent with the NavierStokes equations and present the numerical tests which show that this approximation has a better behavior than the other two. Expand

Stability of pressure boundary conditions for Stokes and Navier-Stokes equations

- Mathematics
- 2001

Abstract The stability of a finite difference discretization of the time-dependent incompressible Navier–Stokes equations in velocity-pressure formulation is studied. In paticular, we compare the… Expand

Consistency Analysis of Finite Difference Approximations to PDE Systems

- Computer Science, Mathematics
- MMCP
- 2011

We consider finite difference approximations to systems of polynomially-nonlinear partial differential equations the coefficients of which are rational functions over rationals in the independent… Expand

Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface

- Physics
- 1965

A new technique is described for the numerical investigation of the time‐dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free. The full… Expand

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

- Mathematics, Computer Science
- ArXiv
- 2006

An algorithmic approach to the generation of fully con- servative difference schemes for linear partial differential equations based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives. Expand

The Method of Differential Approximation

- Mathematics
- 1983

I am very glad that this book is now accessible to English-speaking scientists. During the three years following the publication of the original Russian edition, the method of differential… Expand

Consistency of finite difference approximations for linear PDE systems and its algorithmic verification

- Mathematics, Computer Science
- ISSAC
- 2010

Finite difference approximations for numerical solving of systems of partial differential equations of the form 1-sub = · · · = f<sub><i>p</i></sub> = 0 as approximation of the differential ones are considered. Expand

Computer-Aided Analysis of Difference Schemes for Partial Differential Equations

- Computer Science
- 1996

From the Publisher:
A topical and comprehensive reference containing applications of computerized symbolic manipulations for analyzing the stability of a wide range of diverse schemes commonly used… Expand