Dilation-free solutions for the incompressible flow equations on nonstaggered grids

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 585-586
Author(s):  
P. A. Russell ◽  
S. Abdallah
Keyword(s):  
Incompressible Flow ◽  
Flow Equations

A Jacobian-Free Newton Krylov Implicit-Explicit Time Integration Method for Incompressible Flow Problems

2013 ◽  
Vol 13 (5) ◽  
pp. 1408-1431 ◽  
Author(s):  
Samet Y. Kadioglu ◽  
Dana A. Knoll
Keyword(s):  
Incompressible Flow ◽  
Time Integration ◽  
Order Reduction ◽  
Second Order ◽  
Navier Stokes ◽  
Function Evaluation ◽  
Flow Equations ◽  
Flow Problems ◽  
Specific Operator ◽  
Time Accuracy

AbstractWe have introduced a fully second order IMplicit/EXplicit (IMEX) time in-tegration technique for solving the compressible Euler equations plus nonlinear heat conduction problems (also known as the radiation hydrodynamics problems) in Kadioglu et al., J. Comp. Physics [22,24]. In this paper, we study the implications when this method is applied to the incompressible Navier-Stokes (N-S) equations. The IMEX method is applied to the incompressible flow equations in the following manner. The hyperbolic terms of the flow equations are solved explicitly exploiting the well understood explicit schemes. On the other hand, an implicit strategy is employed for the non-hyperbolic terms. The explicit part is embedded in the implicit step in such a way that it is solved as part of the non-linear function evaluation within the framework of the Jacobian-Free Newton Krylov (JFNK) method [8,29,31]. This is done to obtain a self-consistent implementation of the IMEX method that eliminates the potential order reduction in time accuracy due to the specific operator separation. We employ a simple yet quite effective fractional step projection methodology (similar to those in [11,19,21,30]) as our preconditioner inside the JFNK solver. We present results from several test calculations. For each test, we show second order time convergence. Finally, we present a study for the algorithm performance of the JFNK solver with the new projection method based preconditioner.

Evaluation of an unfactored method for the solution of the incompressible flow equations using artificial compressibility

1998 ◽  
Vol 20 (3) ◽  
pp. 179-187 ◽  
Author(s):  
R.M. Gatiganti ◽  
K.J. Badcock ◽  
F. Cantariti ◽  
L. Dubuc ◽  
M. Woodgate ◽  
...  
Keyword(s):  
Incompressible Flow ◽  
Artificial Compressibility ◽  
Flow Equations

Dilation-Free Solutions for the Incompressible Flow Equations on Nonstaggered Grids

AIAA Journal ◽  
10.2514/2.144 ◽  
1997 ◽  
Vol 35 (3) ◽  
pp. 585-586 ◽  
Author(s):  
P. A. Russell ◽  
S. Abdallah
Keyword(s):  
Incompressible Flow ◽  
Flow Equations

High-Velocity Gas Flow in Reduced Port Valves

1970 ◽  
Vol 92 (4) ◽  
pp. 749-754
Author(s):  
Earl A. Bake
Keyword(s):  
Incompressible Flow ◽  
Gas Flow ◽  
Semiempirical Method ◽  
Compressible Fluids ◽  
Correction Factors ◽  
Flow Rates ◽  
Flow Equations ◽  
Flow Capacity ◽  
Through Flow ◽  
Reduced Port

A semiempirical method has been developed to treat the flow capacity and pressure drop of reduced port, straight-through flow valves handling compressible fluids. Calculations can be based on familiar incompressible flow equations. Correction factors produce results which apply to all gas flow rates up to the critical flow rate of the valve. These corrections will prevent the serious errors which can result from using standard incompressible flow equations alone.

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