The dual integral equation method in hydromechanical systems. (English) Zbl 1083.76048

Kavallaris, N. I.; Zisis, V.

J. Appl. Math. 2004, No. 6, 447-460 (2004).

Summary: Some hydromechanical systems are investigated by applying the dual integral equation method. In developing this method, we suggest from elementary appropriate solutions of Laplace’s equation, in the domain under consideration, the introduction of a potential function which provides useful combinations in cylindrical and spherical coordinate systems. Since the mixed boundary conditions and the form of the potential function are quite general, we obtain integral equations with \(m\)th-order Hankel kernels. We then discuss a kind of approximate practical solutions. We note also that the method has important applications in situations which arise in the determination of the temperature distribution in steady-state heat conduction problems.

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76B10	Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
45F10	Dual, triple, etc., integral and series equations

Keywords:

potential function; Hankel kernels