Implicit solutions of the incompressible Navier-Stokes equations in primitive variables

Mansour, M. L.; Hamed, Almutasim Abdulmuhsin

doi:10.2514/6.1988-717

Cited by 4 publications

(4 citation statements)

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“…It indicates that for Mach numbers of 10~^ and lower, the number of iterations required increases by a factor of more than two. Even with this increase, the algorithm is still very efficient for this range of low Mach numbers, at least compared with the results reported by Mansour and Hamed [63]. As one can expect, the solutions at the above Mach numbers were almost identical since flows at very low Mach numbers are effectively incompressible.…”

Section: Present Results Hwang and Fansupporting

confidence: 73%

“…The geometry of this test case can be seen in Fig [60], [61], [62]. Only a few included solu tions for pressure and heat transfer [63], [64], [65]. For an incompressible flow, it is possible to obtain the pressure from the solution for velocity by solving the pressure Poisson equation.…”

Section: Two-dimensional Compressible Resultsmentioning

confidence: 99%

“…Hamed [63] where a coupled scheme in primitive variables was used for the incom pressible Navier Stokes equations. Usually less than 200 iterations were sufficient to reduce the residual to the desired level.…”

Section: Present Results Hwang and Fanmentioning

confidence: 99%

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A primitive variable, strongly implicit calculation procedure for two and three-dimensional unsteady viscous flows: applications to compressible and incompressible flows including flows with free surfaces

Chen

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Section: Present Results Hwang and Fansupporting

confidence: 73%

Section: Two-dimensional Compressible Resultsmentioning

confidence: 99%

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A primitive variable, strongly implicit calculation procedure for two and three-dimensional unsteady viscous flows: applications to compressible and incompressible flows including flows with free surfaces

Chen

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“…Even with this increase, this algorithm is still very efficient for this range of low-Machnumber cases, at least compared with the results reported by Mansour and Hamed. 28 The solutions for the above Mach numbers were almost identical.…”

mentioning

confidence: 75%

Primitive variable, strongly implicit calculation procedure for viscous flows at all speeds

Chen

Pletcher

1991

AIAA Journal

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A coupled solution procedure is described for solving the compressible form of the time-dependent, twodimensional Navier-Stokes equations in body-fitted curvilinear coordinates. This approach employs the strong conservation form of the governing equations but uses primitive variables (M, v, p, T) rather than the more traditional conservative variables (p, pw, pv, e t ) as unknowns. A coupled modified strongly implicit procedure (CMSIP) is used to efficiently solve the Newton-linearized algebraic equations. It appears that this procedure is effective for Mach numbers ranging from the incompressible limit (M x ~ 0.01) to supersonic. Generally, smoothing was not needed to control spatial oscillations in pressure for subsonic flows despite the use of central differences. Dual-time stepping was found to further accelerate convergence for steady flows. Sample calculations, including steady and unsteady low-Mach-number internal and external flows and a steady shock-boundarylayer interaction flow, illustrate the capability of the present solution algorithm.

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A characteristic‐based method for incompressible flows

Drikakis

Govatsos

Papantonis

1994

Numerical Methods in Fluids

110

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A new characteristic-based method for the solution of the 2D laminar incompressible Navier-Stokes equations is presented. For coupling the continuity and momentum equations, the artificial compressibility formulation is employed. The primitives variables (pressure and velocity components) are defined as functions of their values on the characteristics. The primitives variables on the characteristics are calculated by an upwind differencing scheme based on the sign of the local eigenvalue of the Jacobian matrix of the convective fluxes. The upwind scheme uses interpolation formulae of third-order accuracy. The time discretization is obtained by the explicit Runge-Kutta method. Validation of the characteristic-based method is performed on two different cases: the flow in a simple cascade and the flow over a backwardfacing step.

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Implicit solutions of the incompressible Navier-Stokes equations in primitive variables

Cited by 4 publications

References 0 publications

A primitive variable, strongly implicit calculation procedure for two and three-dimensional unsteady viscous flows: applications to compressible and incompressible flows including flows with free surfaces

A primitive variable, strongly implicit calculation procedure for two and three-dimensional unsteady viscous flows: applications to compressible and incompressible flows including flows with free surfaces

Primitive variable, strongly implicit calculation procedure for viscous flows at all speeds

A characteristic‐based method for incompressible flows

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