An Iterative Finite-Volume Scheme on a Moving Grid. 1st Report. The Fundamental Formulation and Validation.

Abstract

The paper presents a new approach for unsteady coupled system of fluid and body motion of the compressiblie flows on a moving grid system. To assure geometric conservation laws, a finite-volume formulation in the space-time computational domain, of four demension for three-spacial dimensional geometry for example, is adoped in the scheme. The resultant fully implicit scheme is solved iteratively at every time step in order to assure the conservation laws and accuracy. The inner iteration is performed through the efficient and stable Rational Runge-Kutta scheme, so that the algorithm of the scheme can be treated explicitly notwithstanding the implicit scheme. This approach is just the same as pseudo-time concept. This paper gives an interpretation between inner iteration strategy and pseudo-time approach. The basic formulation is given mainly for the one-demensional space in detail in this paper, but the extention to multidimension is straightfoward. The basic feature of the present scheme is investigated and some examples of coupled interaction problemes of fluid and body motion, are given.