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We propose a new algorithm for non-equilibrium molecular dynamics simulationsof thermal gradients. The algorithm is an extension of the heat exchangealgorithm developed by Hafskjold and co-workers [Mol. Phys. 80, 1389 (1993);Mol. Phys. 81, 251 (1994)], in which a certain amount of heat is added to oneregion and removed from another by rescaling velocities appropriately. Sincethe amount of added and removed heat is the same and the dynamics betweenvelocity rescaling steps is Hamiltonian, the heat exchange algorithm isexpected to conserve the energy. However, it has been reported previously thatthe original version of the heat exchange algorithm exhibits a pronounced driftin the total energy, the exact cause of which remained hitherto unclear. Here,we show that the energy drift is due to the truncation error arising from theoperator splitting and suggest an additional coordinate integration step as aremedy. The new algorithm retains all the advantages of the original one whilstexhibiting excellent energy conservation as illustrated for a Lennard-Jonesliquid and SPC/E water.

An enhanced version of the heat exchange algorithm with excellent energy conservation properties