Fourth-Order Compact Schemes for Helmholtz Equations with Piecewise Wave Numbers in the Polar Coordinates

2016 ◽  
Vol 34 (5) ◽  
pp. 499-510 ◽  
Author(s):  
Xiaolu Su ◽  
Xiufang Feng ◽  
Zhilin Li
Keyword(s):  
Fourth Order ◽  
Polar Coordinates ◽  
Compact Schemes ◽  
Helmholtz Equations ◽  
Wave Numbers

Solution of Navier‐Stokes equations by fourth‐order compact schemes and AUSM flux splitting

2006 ◽  
Vol 16 (1) ◽  
pp. 107-120 ◽  
Author(s):  
Mahmood K. Mawlood ◽  
Shahnor Basri ◽  
Waqar Asrar ◽  
Ashraf A. Omar ◽  
Ahmad S. Mokhtar ◽  
...  
Keyword(s):  
Fourth Order ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Compact Schemes ◽  
Navier Stokes Equations ◽  
Flux Splitting

Additional Separated-Variable Solutions of the Biharmonic Equation in Polar Coordinates

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
I. H. Stampouloglou ◽  
E. E. Theotokoglou
Keyword(s):  
Fourth Order ◽  
Biharmonic Equation ◽  
Direct Determination ◽  
Additional Term ◽  
Elastic Solid ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Radial Coordinate ◽  
Displacement Fields ◽  
Polar Coordinate

From the biharmonic equation of the plane problem in the polar coordinate system and taking into account the variable-separable form of the partial solutions, a homogeneous ordinary differential equation (ODE) of the fourth order is deduced. Our study is based on the investigation of the behavior of the coefficients of the above fourth order ODE, which are functions of the radial coordinate r. According to the proposed investigation additional terms, φ¯−m(r,θ)(1≤m≤n) other than the usually tabulated in the Michell solution (1899, “On the Direct Determination of Stress in an Elastic Solid, With Application to the Theory of Plates,” Proc. Lond. Math. Soc., 31, pp. 100–124) are found. Finally the stress and the displacement fields due to each one additional term of φ¯−m(r,θ) are determined.

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