A collocated grid, projection method for time-accurate calculation of low-Mach number variable density flows in general curvilinear coordinates

2012 ◽  
Vol 72 (3) ◽  
pp. 301-319 ◽  
Author(s):  
Mahdi Kooshkbaghi ◽  
Bamdad Lessani
Keyword(s):  
Mach Number ◽  
Projection Method ◽  
Variable Density ◽  
Curvilinear Coordinates ◽  
Accurate Calculation ◽  
Low Mach Number ◽  
Collocated Grid

A Time-Accurate Projection Method for Low-Mach Number Variable Density Flows in Curvilinear Grids

2009 ◽  
Author(s):  
F. N. Fard ◽  
B. Lessani
Keyword(s):  
Mach Number ◽  
Turbulent Flows ◽  
Projection Method ◽  
Time Integration ◽  
Variable Density ◽  
Integration Scheme ◽  
Coordinate Systems ◽  
Low Mach Number ◽  
Curvilinear Coordinate ◽  
Time Integration Scheme

A time-accurate numerical algorithm is proposed for low Mach number variable density flows in curvilinear coordinate systems. In order to increase the stability of the method, a predictor-corrector time integration scheme, coupled with the projection method, is employed. The projection method results in a constant-coefficient Poisson equation for the pressure in both the predictor and corrector steps. The continuity equation is fully satisfied at each step. To prevent the pressure odd-even decoupling typically encountered in collocated grids, a flux interpolation technique is developed. The spatial discretization method offers computational simplicity and straightforward extension to 3D curvilinear coordinate systems, which are essential in the simulation of turbulent flows in complex geometries. The accuracy and stability of the algorithm are tested with a series of numerical experiments, and the results are validated against the available data in the literature.

scholarly journals A half-explicit, non-split projection method for low Mach number flows.

2004 ◽  
Author(s):  
Jerome G. Pousin ◽  
Habib N. Najm ◽  
Philippe Pierre Pebay
Keyword(s):  
Mach Number ◽  
Projection Method ◽  
Low Mach Number

scholarly journals An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion

1998 ◽  
Vol 140 (1-6) ◽  
pp. 123-168 ◽  
Author(s):  
R. B. PEMBER ◽  
L. H. HOWELL ◽  
J. B. BELL ◽  
P. COLELLA ◽  
W. Y. CRUTCHFIELD ◽  
...  
Keyword(s):  
Mach Number ◽  
Projection Method ◽  
Low Mach Number

Projection method for high-order compact schemes for low Mach number flows in enclosures

2014 ◽  
Vol 24 (5) ◽  
pp. 1141-1174 ◽  
Author(s):  
Artur Tyliszczak
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Projection Method ◽  
High Order ◽  
Staggered Grid ◽  
Constant Density ◽  
Computational Domain ◽  
Content Type ◽  
Low Mach Number ◽  
Large Density

Purpose – Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low Mach number flows with large density and temperature variations. Design/methodology/approach – Low Mach number approximation approach is used in the paper combined with a predictor-corrector method and accurate compact scheme of fourth and sixth order. A novel algorithm is formulated for the projection method in which the boundary conditions for the pressure are implemented in such a way that the continuity equation is fulfilled everywhere in the computational domain, including the boundary nodes. Findings – It is shown that proposed implementation of the boundary conditions considerably improves a solution accuracy. Assessment of the accuracy was performed based on the constant density Burggraf flow and for two benchmark cases for the natural convection problems: steady flow in a square cavity and unsteady flow in a tall cavity. In all the cases the results agree very well with exemplary solutions. Originality/value – A staggered or half-staggered grid arrangement is usually used for the projection method for both constant and low Mach number flows. The staggered approach ensures stability and strong pressure-velocity coupling. In the paper a high-order compact method has been implemented in the framework of low Mach number approximation on collocated meshes. The resulting algorithm is accurate, robust for large density variations and is almost free from the pressure oscillations.

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