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 of mass, momentum, and energy. We also discuss the special cases of the Navier-Stokes equations for viscous flow and the Fourier law for thermal 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.

• Received 19 December 1997

DOI:https://doi.org/10.1103/PhysRevE.58.1843