The uniqueness of the solution of the two-dimensional direct problem of a wave process with an instantaneous source and a flat boundary

2018 ◽  
Author(s):  
Abdugany Dj. Satybaev ◽  
Yuliya V. Anishchenko ◽  
Ainagul Zh. Kokozova ◽  
Amangeldi A. Alimkanov
Keyword(s):  
Direct Problem ◽  
Wave Process ◽  
Two Dimensional ◽  
Uniqueness Of The Solution ◽  
Instantaneous Source

Numerical solution of a two-dimensional direct problem of the wave process

2018 ◽  
Author(s):  
Abdugany Djunusovich Satybaev ◽  
Ainagul Zhylkychyevna Kokozova ◽  
Yuliya Vladimirovna Anishchenko ◽  
Amangeldi Arapbaevich Alimkanov
Keyword(s):  
Numerical Solution ◽  
Direct Problem ◽  
Wave Process ◽  
Two Dimensional

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

A Linearized Two-Dimensional Theory for High-Speed Hydrofoils Near the Free Surface

1966 ◽  
Vol 10 (01) ◽  
pp. 25-48
Author(s):  
Richard P. Bernicker
Keyword(s):  
Direct Problem ◽  
High Speed ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Pressure Loading ◽  
Dimensional Theory ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Sectional Shape ◽  
Infinite Set

A linearized two-dimensional theory is presented for high-speed hydrofoils near the free surface. The "direct" problem (hydrofoil shape specified) is attacked by replacing the actual foil with vortex and source sheets. The resulting integral equation for the strength of the singularity distribution is recast into an infinite set of linear algebraic equations relating the unknown constants in a Glauert-type vorticity expansion to the boundary condition on the foil. The solution is achieved using a matrix inversion technique and it is found that the matrix relating the known and unknown constants is a function of depth of submergence alone. Inversion of this matrix at each depth allows the vorticity constants to be calculated for any arbitrary foil section by matrix multiplication. The inverted matrices have been calculated for several depth-to-chord ratios and are presented herein. Several examples for specific camber and thickness distributions are given, and results indicate significant effects in the force characteristics at depths less than one chord. In particular, thickness effects cause a loss of lift at shallow submergences which may be an appreciable percentage of the total design lift. The second part treats the "indirect" problem of designing a hydrofoil sectional shape at a given depth to achieve a specified pressure loading. Similar to the "direct" problem treated in the first part, integral equations are derived for the camber and thickness functions by replacing the actual foil by vortex and source sheets. The solution is obtained by recasting these equations into an infinite set of linear algebraic equations relating the constants in a series expansion of the foil geometry to the known pressure boundary conditions. The matrix relating the known and unknown constants is, again, a function of the depth of submergence alone, and inversion techniques allow the sectional shape to be determined for arbitrary design pressure distributions. Several examples indicate the procedure and results are presented for the change in sectional shape for a given pressure loading as the depth of submergence of the foil is decreased.

On the speed of progressive waves in gust-tunnels of the QMC-type

1987 ◽  
Vol 91 (907) ◽  
pp. 321-332
Author(s):  
M. S. Ishaq ◽  
L. Bernstein
Keyword(s):  
Wind Tunnel ◽  
Wave Process ◽  
Unsteady Flows ◽  
Travelling Wave ◽  
Two Dimensional ◽  
Queen Mary College ◽  
Wave Type ◽  
Open Test ◽  
Progressive Waves ◽  
Low Speed Wind Tunnel

SummaryIn the Queen Mary College gust-tunnels, unsteady flows are generated by oscillating flaps attached to the downstream upper and lower surfaces of the contraction nozzle of a semi-open test section, open-return, low-speed wind-tunnel. The flow perturbations produced on the mainstream of velocityU∞, are of the travelling-wave type, with wave-velocityQ. Attention is drawn to the contradictory early measurements ofQ/U∞. New data are presented which showQ/U∞apparently diminishing along the tunnel axis from a high value near the nozzle exit to an asymptotic value of about 0·6 far downstream. Using a digital phase meter especially developed for the purpose it is shown that the explanation for this behaviour lies in the two-dimensional nature of the wave process in the region of the flaps.

Compressible Subsonic Flow in Two-dimensional Channels

1955 ◽  
Vol 6 (3) ◽  
pp. 205-220 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Conformal Mapping ◽  
Direct Problem ◽  
Subsonic Flow ◽  
Ideal Gas ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Step Functions ◽  
Curved Walls ◽  
Special Case ◽  
The Ideal

SummaryEquations for the calculation of the subsonic flow of an inviscid fluid through given two-dimensional channels (the “ direct” problem), and for the design (the “ indirect” problem) of such channels are derived. The method is based on conformal mapping, and in the special case of channels with walls made from a number of straight sections, or with wall pressure prescribed as step-functions, yields the same results as the well-known Schwarz-Christoffel mapping theorem technique. However, it is more general than this latter method, since it is capable of dealing with curved walls or continuously varying wall pressures. The compressibility of the fluid is allowed for only approximately, the ideal gas being replaced by a Kàrmàn-Tsien tangent gas.In Part II the theory is applied to various problems of aeronautical interest, perhaps the most important of which is to the setting of “ streamlined ” walls about a symmetrical aerofoil placed in the centre of the channel.

scholarly journals Numerical Solution of Two-Dimensional Fredholm–Volterra Integral Equations of the Second Kind

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1326
Author(s):  
Sanda Micula
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Cubature Formula ◽  
Volterra Integral Equations ◽  
Picard Iteration ◽  
Successive Approximations ◽  
Future Research ◽  
Two Dimensional ◽  
Uniqueness Of The Solution

The paper presents an iterative numerical method for approximating solutions of two-dimensional Fredholm–Volterra integral equations of the second kind. As these equations arise in many applications, there is a constant need for accurate, but fast and simple to use numerical approximations to their solutions. The method proposed here uses successive approximations of the Mann type and a suitable cubature formula. Mann’s procedure is known to converge faster than the classical Picard iteration given by the contraction principle, thus yielding a better numerical method. The existence and uniqueness of the solution is derived under certain conditions. The convergence of the method is proved, and error estimates for the approximations obtained are given. At the end, several numerical examples are analyzed, showing the applicability of the proposed method and good approximation results. In the last section, concluding remarks and future research ideas are discussed.

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