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Concept
Energy drift
Summary
In computer simulations of mechanical systems, energy drift is the gradual change in the total energy of a closed system over time. According to the laws of mechanics, the energy should be a constant of motion and should not change. However, in simulations the energy might fluctuate on a short time scale and increase or decrease on a very long time scale due to numerical integration artifacts that arise with the use of a finite time step Δt. This is somewhat similar to the flying ice cube problem, whereby numerical errors in handling equipartition of energy can change vibrational energy into translational energy.
More specifically, the energy tends to increase exponentially; its increase can be understood intuitively because each step introduces a small perturbation δv to the true velocity vtrue, which (if uncorrelated with v, which will be true for simple integration methods) results in a second-order increase in the energy
(The cross term in v · δv is zero because of no correlation.)
Energy drift - usually damping - is substantial for numerical integration schemes that are not symplectic, such as the Runge-Kutta family. Symplectic integrators usually used in molecular dynamics, such as the Verlet integrator family, exhibit increases in energy over very long time scales, though the error remains roughly constant. These integrators do not in fact reproduce the actual Hamiltonian mechanics of the system; instead, they reproduce a closely related "shadow" Hamiltonian whose value they conserve many orders of magnitude more closely. The accuracy of the energy conservation for the true Hamiltonian is dependent on the time step. The energy computed from the modified Hamiltonian of a symplectic integrator is from the true Hamiltonian.
Energy drift is similar to parametric resonance in that a finite, discrete timestepping scheme will result in nonphysical, limited sampling of motions with frequencies close to the frequency of velocity updates.
Official source
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