An investigation of dissipative forces for Lagrangian computational fluid dynamics is conducted from Hamiltonian considerations including energy dissipation for macroscopic systems. It is shown that discrete forces must fulfill particular rules to be in agreement with the fundamentals of Physics. Those rules are specified in the case of the smoothed particle hydrodynamics (SPH) numerical approach, leading to a clear treatment of friction forces in connection with energy dissipation. In particular, it is proved that the kernel function, which is at the heart of interpolation in SPH, must satisfy some constraints in order to be consistent with the dissipative properties of a real fluid. A numerical example is given to illustrate the abovementioned considerations.

• Received 21 October 2008

DOI:https://doi.org/10.1103/PhysRevE.80.036705