Solutions of the Laplace equation in cylindrical coordinates, driven to 2D harmonic potentials

2020 ◽  
pp. 181-193
Author(s):  
Igor F. Spivak-Lavrov ◽  
Telektes Zh. Shugaeva ◽  
Samat U. Sharipov
Keyword(s):  
Laplace Equation ◽  
Cylindrical Coordinates

scholarly journals SOLUTIONS OF THE LAPLACE EQUATION IN CYLINDRICAL COORDINATES, REDUCED TO TWO-DIMENSIONAL HARMONIC POTENTIALS

2020 ◽  
Vol 30 (2) ◽  
pp. 51-60
Author(s):  
I. F. Spivak-Lavrov ◽  
◽  
S. U. Sharipov ◽  
T. Zh. Shugaeva ◽  
◽  
...  
Keyword(s):  
Laplace Equation ◽  
Two Dimensional ◽  
Cylindrical Coordinates

The study of the process of evolution of the jet under outflow of water from the supercritical state through a thin nozzle

2016 ◽  
Vol 11 (1) ◽  
pp. 66-71 ◽  
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Korobchinskaya
Keyword(s):  
Stationary Process ◽  
Supercritical State ◽  
System Of Differential Equations ◽  
Jet Formation ◽  
Cylindrical Coordinates ◽  
Initial Stage ◽  
Supersonic Regime ◽  
Water Outflow ◽  
Thin Nozzle ◽  
Supercritical Temperature

The dynamics of the water outflow from the initial supercritical state through a thin nozzle is studied. To describe the initial stage of non-stationary process outflow the system of differential equations of conservation of mass, momentum and energy in a two-dimensional cylindrical coordinates with axial symmetry is used. The spatial distribution of pressure and velocity of jet formation was received. It was established that a supersonic regime of outflow at supercritical temperature of 650 K is formed, which have a qualitative agreement for the velocity compared with the Bernoulli analytical solution and the experimental data.

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

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