DISCRETE MODELING OF LOSSLESS FLUID DYNAMIC-SYSTEMS

An attractive new approach for numerically integrating the partial differential equations of passive dynamical system consists in modelling the continuous-domain system by means of a discrete multidimensionally passive (MD-passive) dynamical system. This can be achieved by first deriving an appropriate MD-passive Kirchhoff circuit and by applying, to this circuit, principles as known from the theory of multidimensional wave digital filters. While the method had previously been applied to linear problems, it is shown that it can also be used for the strongly nonlinear equations of fluid dynamics. All major features such as inherent massive parallelism, exclusively local nature of the interdepencies, high robustness etc. are preserved. The essential principles for arriving at the desired solution are described, although further details, including the specific treatment of the viscous case, are left for future publications.