DISCRETIZED INTEGRAL HYDRODYNAMICS

Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid . In the appropriate limit, these become the usual conservation laws o f mass, momentum, and energy. We also discuss the special cases of the Navier-Stokes equations for viscous flow and the Fourier law for ther mal conduction in the presence of hydrodynamic fluctuations. By means of a discretization procedure, we show how the integral equations can give rise to the so-called ''particle dynamics'' of smoothed particle hydrodynamics and dissipative particle dynamics.