A STOCHASTIC APPROACH TO COMPUTATIONAL FLUID-DYNAMICS

In this paper a new approach to computational fluid dynamics is introduced in which the fluid is regarded as a stochastic dynamical system. The velocity of the fluid is related to a stochastic process governed by an appropriate master equation acting in a discrete phase space. The method is explained by means of (1 + 1)-dimensional flow phenomena. It is shown that the stochastic approach naturally leads to transparent numerical algorithms for stochastic simulations of fluid motion. By simulating plane Poiseuille flow it is demonstrated that the probabilistic approach yields a correct description of laminar fluid motion. Furthermore, soliton-like and shock wave solutions of Burgers' equation are generated by stochastic simulations of the underlying stochastic process.