An Approximate Solution Technique for the Flow Past an Obstacle with a Large Weber Number

2022 ◽  
Vol 8 (1) ◽  
Author(s):  
May Manal Bounif ◽  
Abdelkader Gasmi
Keyword(s):  
Approximate Solution ◽  
Weber Number ◽  
Solution Technique ◽  
Flow Past

The influence of surface tension on cavitating flow past a curved obstacle

1983 ◽  
Vol 133 ◽  
pp. 255-264 ◽  
Author(s):  
Jean-Marc Vanden-Broeck
Keyword(s):  
Boundary Condition ◽  
Surface Tension ◽  
Contact Angle ◽  
Circular Cylinder ◽  
Classical Solution ◽  
Weber Number ◽  
Cavitating Flow ◽  
Two Dimensional ◽  
Dynamic Boundary Condition ◽  
Flow Past

The problem of cavitating flow past a two-dimensional curved obstacle is considered. Surface tension is included in the dynamic boundary condition. A perturbation solution for small values of the surface tension is presented. It is found that the position of the separation points is uniquely determined by specifying the value of the Weber number and the contact angle at the separation points. In addition, for a given value of the Weber number there exists a particular position of the separation points for which the slope is continuous. This solution tends to the classical solution satisfying the Brillouin–Villat condition as the surface tension tends to zero. Graphs of the results for the cavitating flow past a circular cylinder are presented.

scholarly journals Approximate Solution Technique for Singular Fredholm Integral Equations of the First Kind with Oscillatory Kernels

2019 ◽  
pp. 1-9
Author(s):  
Vivian Ndfutu Nfor ◽  
George Emese Okecka
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Legendre Polynomials ◽  
Lagrange Interpolation ◽  
Interpolation Formula ◽  
Verification And Validation ◽  
Solution Technique ◽  
Fredholm Integral Equations ◽  
Lagrange Interpolation Formula ◽  
Interpolation Nodes

An efficient quadrature formula was developed for evaluating numerically certain singular Fredholm integral equations of the first kind with oscillatory trigonometric kernels.  The method is based on the Lagrange interpolation formula and the orthogonal polynomial considered are the Legendre polynomials whose zeros served as interpolation nodes. A test example was provided for the verification and validation of the rule developed. The results showed the convergence of the solution and can be improved by increasing n.

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