Three-dimensional grid generation using poisson equations

1982 ◽  
Vol 10-11 ◽  
pp. 687-694 ◽  
Author(s):  
C.F. Shieh
2021 ◽  
Vol 10 (1) ◽  
pp. 1356-1383
Author(s):  
Yong Wang ◽  
Wenpei Wu

Abstract We study the initial-boundary value problems of the three-dimensional compressible elastic Navier-Stokes-Poisson equations under the Dirichlet or Neumann boundary condition for the electrostatic potential. The unique global solution near a constant equilibrium state in H 2 space is obtained. Moreover, we prove that the solution decays to the equilibrium state at an exponential rate as time tends to infinity. This is the first result for the three-dimensional elastic Navier-Stokes-Poisson equations under various boundary conditions for the electrostatic potential.


Author(s):  
Guy Phuong ◽  
Sylvester Abanteriba ◽  
Paul Haley ◽  
Philippe Guillerot

Volutes are widely used in centrifugal compressors for industrial processes, refrigeration systems, small gas turbines and gas pipelines. However, large costs associated with the volute design and analysis process can be reduced with the introduction of a software design system that ties together both geometry creation and mesh generation having the ultimate intent of improving stage efficiency. Computational Fluid Dynamics (CFD) has become an integral part of engineering design. High quality grids need to be produced as part of the analysis process. Engineers of different expertise may be required to determine volute design constraints and parameters, produce the geometry, and generate a high quality grid. The current research aims to develop and demonstrate a volute design tool that allows design engineers the ability to easily and efficiently generate volute geometry and automate grid generation by means of geometrical constraints using functional relationships. The approach was outlined in [1]. Visualization of volute geometry can be in two-dimensional (2D) or three-dimensional (3D) modes. Control of the diffuser upstream of the scroll, the scroll itself and the conic are totally integrated in the design system. The user can position the conic anywhere in space and control the shape of the conic centroid curve, therefore having complete control over the development of the tongue region. The program will output data for automated grid generation where user can control resulting grid properties. Once the desired design configuration has been determined, the users can output the geometry surfaces and wireframes to a Computer Aided Design (CAD) package for production. Every little detail is also incorporated into the software from volute draft angle, discharge conic centroid shape, to cross section fillet radii. Upon entering all the required constraints and parameters of the volute, the geometry is created in seconds. Grids can be generated in minutes accommodating geometrical changes thus reducing the bottlenecks associated with geometry/grid generation for CFD applications.


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