scholarly journals Pressure segregation methods based on a discrete pressure Poisson equation. An algebraic approach

2008 ◽  
Vol 56 (4) ◽  
pp. 351-382 ◽  
Author(s):  
Santiago Badia ◽  
Ramon Codina
Keyword(s):  
Poisson Equation ◽  
Algebraic Approach ◽  
Pressure Poisson Equation

scholarly journals Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 269 ◽  
Author(s):  
Xiaojing Zhang ◽  
Vladimir Gerdt ◽  
Yury Blinkov
Keyword(s):  
Difference Scheme ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Integrability Condition ◽  
Three Dimensional ◽  
Algebraic Approach ◽  
Second Order ◽  
Algebraic Construction ◽  
Pressure Poisson Equation ◽  
Strongly Consistent

By using symbolic algebraic computation, we construct a strongly-consistent second-order finite difference scheme for steady three-dimensional Stokes flow and a Cartesian solution grid. The scheme has the second order of accuracy and incorporates the pressure Poisson equation. This equation is the integrability condition for the discrete momentum and continuity equations. Our algebraic approach to the construction of difference schemes suggested by the second and the third authors combines the finite volume method, numerical integration, and difference elimination. We make use of the techniques of the differential and difference Janet/Gröbner bases for performing related computations. To prove the strong consistency of the generated scheme, we use these bases to correlate the differential ideal generated by the polynomials in the Stokes equations with the difference ideal generated by the polynomials in the constructed difference scheme. As this takes place, our difference scheme is conservative and inherits permutation symmetry of the differential Stokes flow. For the obtained scheme, we compute the modified differential system and use it to analyze the scheme’s accuracy.

Determination of the Pressure Field Using Three-Dimensional, Volumetric Velocity Measurements

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Hansheng Pan ◽  
Sheila H. Williams ◽  
Paul S. Krueger
Keyword(s):  
Poisson Equation ◽  
Temporal Resolution ◽  
Pressure Field ◽  
Three Dimensional ◽  
Vortical Flow ◽  
Flow Conditions ◽  
Velocity Measurements ◽  
Pressure Poisson Equation ◽  
Computational Fluid Dynamics Cfd

Methods to determine the pressure field of vortical flow from three-dimensional (3D) volumetric velocity measurements (e.g., from a TSI V3VTM system) are discussed. The boundary pressure was determined where necessary using the unsteady Bernoulli equation for both line integration and pressure Poisson equation methods. Error analysis using computational fluid dynamics (CFD) data was conducted to investigate the effects of spatial resolution, temporal resolution, and velocity error levels. The line integration method was more sensitive to temporal resolution, while the pressure Poisson equation method was more sensitive to boundary flow conditions. The latter was generally more suitable for V3VTM velocity measurements.

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