Predictions of fluid flow and heat transfer problems by the vorticity-velocity formulation of the Navier-Stokes equations

Fusegi, Toru; Farouk, Bakhtier

doi:10.1016/0021-9991(86)90013-6

Cited by 16 publications

(21 citation statements)

References 13 publications

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“…As explained by Fusegi and Farouk [14], from the 'maximum principle' it follows that D is maximal on the boundary. It can be concluded that continuity (D= 0) is ensured in the entire integration domain if it is satisfied on the boundary of the problem.…”

Section: Governing Equationsmentioning

confidence: 89%

“…For the velocity -vorticity formulation, there are certain aspects to be noted [1,14]. Even though the continuity equation has been assumed to be satisfied for the derivation of velocity Poisson equations (9) and (10), it may not be necessarily guaranteed for the integral or difference equations based on the velocity -vorticity formulation.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Hence, if care is taken to satisfy the continuity condition to a high degree of accuracy on the boundaries, mass conservation is ensured to an even higher accuracy in the interior of the integration domain of the problem. The vorticity definition can be considered in a similar way [1,14]. For the class of problem analyzed in the present investigations, and by the assumption of no-slip walls on the boundaries, the continuity condition is automatically satisfied.…”

Section: Governing Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Solution of the Navier-Stokes equations in velocity-vorticity form using a Eulerian-Lagrangian boundary element method

Young

Yang

Eldho

2000

Int. J. Numer. Meth. Fluids

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Section: Governing Equationsmentioning

confidence: 89%

Section: Governing Equationsmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Solution of the Navier-Stokes equations in velocity-vorticity form using a Eulerian-Lagrangian boundary element method

Young

Yang

Eldho

2000

Int. J. Numer. Meth. Fluids

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“…So, from the 'maximum principle', we know that f should be maximal at a boundary [88]. Consequently, as discussed in [33,34], employing continuity as a BC can effectively reduce the magnitude of f to approximately zero throughout the domain and consequently improve mass conservation of the ORIG solution.…”

Section: Application 2: Axisymmetric Laminar Diffusion Flame In An Unmentioning

confidence: 98%

MC-Smooth: A mass-conserving, smooth vorticity–velocity formulation for multi-dimensional flows

Cao

Bennett

Smooke

2015

Combustion Theory and Modelling

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A novel vorticity-velocity formulation of the Navier-Stokes equations -the MassConserving, Smooth (MC-Smooth) vorticity-velocity formulation -is developed in this work. The governing equations of the MC-Smooth formulation include a new secondorder Poisson-like elliptic velocity equation, along with the vorticity transport equation, the energy conservation equation, and N spec species mass balance equations. In this study, the MC-Smooth formulation is compared to two pre-existing vorticity-velocity formulations by applying each formulation to confined and unconfined axisymmetric laminar diffusion flame problems. For both applications, very good to excellent agreement for the simulation results of the three formulations has been obtained. The MC-Smooth formulation requires the least CPU time and can overcome the limitations of the other two pre-existing vorticity-velocity formulations by ensuring mass conservation and solution smoothness over a broader range of flow conditions. In addition to these benefits, other important features of the MC-Smooth formulation include: (1) it does not require the use of a staggered grid, and (2) it does not require excessive grid refinement to ensure mass conservation. The MC-Smooth formulation is a computationally attractive approach that can effectively extend the applicability of the vorticity-velocity formulation.

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“…Schreiber and Keller [2] described a combination of numerical techniques for solving the steady plane incompressible Navier-Stokes equations and, as an illustration, used them to compute accurate solutions for the driven cavity flow problems. Fusegi and Bakhtierfarouk [4] investigated some predictions of fluid flow and heat transfer using the vorticity-velocity formulation. The problem of steady incompressible Navier-Stokes equations of a 2-D driven cavity flow with an efficient method has been investigated by Bruneau and Jouron [6].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of 2-D Unsteady Incompressible Flow in a Driven Square Cavity Using Streamfunction-Vorticity Formulation

Ambethkar¹,

Kumar²,

Srivastava³

2016

Int. J. of Appl. Math.

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In this paper, we have used a streamfunction-vorticity (ψ − ξ) formulation to investigate the problem of 2-D unsteady viscous incompressible flow in a driven square cavity with moving top and bottom walls. We used this formulation to solve the governing equations along with no-slip and slip wall boundary conditions. A general algorithm was used for this formulation in order to compute the numerical solutions for the flow variables: streamfunction ψ, vorticityfunction ξ for low Reynolds numbers Re ≤ 50. We have executed this with the aid of a computer programme developed and run in C++ compiler. We have proved the stability and convergence of the numerical scheme using matrix method. Following this, the stability conditions obtained for the time and space steps have been used in numerical computations to arrive at the numerical solutions with desired accuracy. Also investigated was the variation of u and v components of velocity at points closed to left side, top and bottom walls of the square cavity at different time levels for Reynolds number 50. Based on the numerical computations of u-velocity, we found: (i) the u-velocity is almost same near the top and bottom wall of the square cavity above and below the geometric center for Re=15 and 30; (ii) the absolute value of the u-velocity first decreases, then increases, and finally decreases, near top and bottom wall of the square cavity. Based on the numerical computations of the v-velocity, we found: (i) the absolute value of the v-velocity increases uniformly as time level increases' (ii) the v-velocity at the right wall of the square cavity attains a maximum value, and then, decreases towards the geometric center. The numerical solutions of the vorticity vector ξ at Re=50 for different times along the horizontal line through geometric center of the square cavity indicate the following: (i) the vorticity contours decreased in between the left wall boundary to the midpoint of the square domain; (ii) it, then, increased in between the midpoint to the right wall boundary. Based on the numerical solutions of streamfunction ψ, we found: (i) the size of streamline contours decreased when the time increased; (ii) two streamline contours are generated, one above the geometric center, and the other, below the geometric center in clockwise direction.

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Predictions of fluid flow and heat transfer problems by the vorticity-velocity formulation of the Navier-Stokes equations

Cited by 16 publications

References 13 publications

Solution of the Navier-Stokes equations in velocity-vorticity form using a Eulerian-Lagrangian boundary element method

Solution of the Navier-Stokes equations in velocity-vorticity form using a Eulerian-Lagrangian boundary element method

MC-Smooth: A mass-conserving, smooth vorticity–velocity formulation for multi-dimensional flows

Numerical Solutions of 2-D Unsteady Incompressible Flow in a Driven Square Cavity Using Streamfunction-Vorticity Formulation

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