A sparse grid method for the Navier-Stokes equations based on hyperbolic cross

2013 ◽  
Vol 37 (6) ◽  
pp. 870-881
Author(s):  
Qingfang Liu ◽  
Lei Ding ◽  
Qingchang Liu
Keyword(s):  
Stokes Equations ◽  
Grid Method ◽  
Sparse Grid ◽  
Navier Stokes ◽  
Hyperbolic Cross ◽  
Navier Stokes Equations ◽  
Sparse Grid Method

Modeling coherent structures in the atmosphere and assessing their impact on aircraft

2021 ◽  
Author(s):  
V.V. Vyshinsky ◽  
K.T. Zoan
Keyword(s):  
Stokes Equations ◽  
Grid Method ◽  
Computer Code ◽  
Light Transport ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Structures ◽  
Glide Path ◽  
Coherent Vortex ◽  
Coherent Vortex Structure

The paper introduces an engineering method for assessing the aerodynamic effect of disturbed atmosphere on an aircraft. As a source of vortex structures, we can consider vortex wind wakes that arise when the atmospheric wind flows around the landscape, large structures, moving or stationary aircraft-carrying platforms, vortex wakes behind aircraft, etc. In this study, we consider the situation when a light transport aircraft and an aircraft of the MC-21 type get into the vortex wake behind the super-heavy aircraft A-380 when flying along the glide path. A coherent vortex structure behind the A-380 is formed by the grid method within the framework of the boundary value problem for the Reynolds-averaged Navier —Stokes equations. The evolution and stochastics of the far wake are carried out using the author’s computer code written in the MATLAB system, within the framework of discrete vortices with a Rankine core. The assessment of the increment of forces and moments from the effect of the vortex system on the aircraft was carried out using the panel method.

scholarly journals Application of Multi-Grid Methods for Solving the Navier-Stokes Equations

1989 ◽  
Vol 203 (4) ◽  
pp. 255-265 ◽  
Author(s):  
A O Demuren
Keyword(s):  
Approximation Scheme ◽  
Stokes Equations ◽  
Grid Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Relaxation Scheme ◽  
Grid Approach ◽  
Grid Technique ◽  
Point Line

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

scholarly journals Recirculating flows analysis and estimation inside channels

2018 ◽  
Vol 172 ◽  
pp. 01001
Author(s):  
Christina G. Georgantopoulou ◽  
Nikolaos S. Vasilikos ◽  
George A. Georgantopoulos
Keyword(s):  
Stokes Equations ◽  
Grid Method ◽  
Reynolds Numbers ◽  
Industrial Applications ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Inlet Flow Rate ◽  
Inclination Angles ◽  
Exact Position ◽  
Recirculation Zones

The recirculation which is developed during the flows inside pipes present a high interest in many industrial applications. In the present paper, a Cartesian grid method is presented which can be applied in pipes geometry approximation, even if the solid bounds are not lying on grid lines. A refinement technique using rectangular nested sub-girds is applied in order to avoid the unnecessary grid cells in the areas with no particular flow interest and cluster the grid when is needed. Important and useful for the industries results are extracted by these numerical simulations and estimations regarding the exact position and extend of the recirculation zones and the relating points. The estimation is taking placefor incompressible laminar, viscous flows inside inclined step channelsfor a range of inclination angles and Reynolds numbers values. The Navier – Stokes equations are solved using the artificial compressibility method according to the necessary boundary conditions arrangement. Flow results are presented for several grid sizes and Reynolds numbers focused on the recirculationzones length, in upper and lower channel’ walls. Accepted accuracy of the flow results is produced using the aforementioned refinement algorithm, while the flow zones can be located according to the inlet flow rate, in order to avoid possible problems in the industries as corrosion or energy losses.

scholarly journals FLOW DYNAMIC COMPARISON BETWEEN RECESSED HINGE AND OPEN PIVOT BI-LEAFLET HEART VALVE DESIGNS

2009 ◽  
Vol 09 (02) ◽  
pp. 161-176 ◽  
Author(s):  
V. GOVINDARAJAN ◽  
H. S. UDAYKUMAR ◽  
K. B. CHANDRAN
Keyword(s):  
Heart Valve ◽  
Stokes Equations ◽  
Mechanical Heart Valve ◽  
Grid Method ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Particle Interactions ◽  
Navier Stokes Equations ◽  
Valve Function ◽  
Solution Accuracy

The flow dynamics through the peripheral and hinge regions of a bi-leaflet mechanical heart valve are complex and result in abnormally high shear stresses particularly during the closing phase of the valve function. It has been observed that the late stages of closure are more significant in the dynamics of platelet activation; therefore, the later stages of closure are simulated by solving the two-dimensional Navier–Stokes equations using an Eulerian Levelset-based sharp interface Cartesian grid method. Using a fixed Cartesian mesh incorporating local mesh refinement for solution accuracy and efficiency, the flow-through within a recessed hinge design and an open pivot hinge design is compared. Platelets are modeled as point particles by Lagrangian particle tracking algorithm with one way coupling. A dilute particle flow is assumed and particle–particle interactions are neglected. It was observed that the hinge region of the open pivot valve indicated a lower potential for activation of platelets compared to that in valves with a recessed hinge design.

AN AUGMENTED PROJECTION METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN ARBITRARY DOMAINS

2005 ◽  
Vol 02 (02) ◽  
pp. 201-212 ◽  
Author(s):  
JUNSEOK KIM
Keyword(s):  
Velocity Field ◽  
Projection Method ◽  
Vector Fields ◽  
Stokes Equations ◽  
Grid Method ◽  
Cartesian Grid ◽  
Moving Boundaries ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Divergence Free Vector

A Cartesian grid method for computing flows with complex immersed, stationary and moving boundaries is presented in this paper. We introduce an augmented projection method for the numerical solution of the incompressible Navier-Stokes equations in arbitrary domains. In a projection method an intermediate velocity field is calculated from the momentum equations, which is then projected onto the space of divergence-free vector fields. In the proposed augmented projection method, we add one more step, which effectively eliminates spurious velocity field caused by complex immersed moving boundaries. The methodology is validated by comparing it with analytic, previous numerical and experimental results.

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