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Discretized integral hydrodynamics

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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.

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ROMERO-ROCHÍN, V. and RUBÍ CAPACETI, José Miguel. Discretized integral hydrodynamics. Physical Review E. 1998. Vol. 58, num. 2, pags. 1843. ISSN 1063-651X. [consulted: 23 of May of 2026]. Available at: https://hdl.handle.net/2445/18792

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