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Article information
2001 , Volume 6, ¹ 4, p.92-119
Christo C.I., Marinova R.S.
Implicit vectorial operator splitting for incompressible Navier-Stokes equations in primitive variables
The steady incompressible Navier-Stokes equations in primitive variables are coupled by a Poisson equation for the pressure from which the continuity equation is subtracted. The equivalence to the original N-S problem is proved. Fictitious time is added and vectorial operator-splitting is employed leaving the system coupled at each fractional-time step which allows satisfying the boundary conditions without introducing artificial condition for the pressure. Conservative second-order approximations for the convective terms are employed on a staggered grid. The lid-driven 2D flow in a rectangular cavity is considered as a featuring example. Laminar flow is obtained in our computations for Reynolds numbers up to Re=11,000 on grids with up to 512x512 cells. The results obtained on different grids confirm the consistency and convergence of the scheme. The flow characteristics calculated here are in very good quantitative agreement with the available numerical solutions form the literature for Re<=10,000.
[full text] Classificator Msc2000:- *76D05 Navier-Stokes equations
- 76M20 Finite difference methods
Keywords: incompressible Navier-Stokes equations, primitive variables, lid-driven cavity flow, quasi-stationary method, rectangular cavities, incompressibility constraint, Poisson equation, pressure, stability, continuity condition, vectorial implicit operator-splitting method, conservative central differences, consistency, convergence
Author(s):
Christo Christov Ivanov
Office: Department of Mathematics, University of Louisiana at Lafayette
Address: USA, Louisiana
E-mail: christov@louisiana.edu
Marinova R S
Office: Dept. of Mathematics, Free University of Varna
Address: Bulgaria, Varna, Varna 9007
Bibliography link:
Christo C.I., Marinova R.S. Implicit vectorial operator splitting for incompressible Navier-Stokes equations in primitive variables // Computational technologies. 2001. V. 6. ¹ 4. P. 92-119
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