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Energy methods for constructing time-stepping algorithms are of increasedinterest in application to nonlinear problems, since numerical stability can beinferred from the conservation of the system energy. Alternatively, symplecticintegrators may be constructed that preserve the symplectic form of the system.This methodology has been established for Hamiltonian systems, with numerousapplications in engineering problems. In this paper an extension of suchmethods to non-conservative acoustic systems is presented. Discreteconservation laws, equivalent to that of energy-conserving schemes, are derivedfor systems with linear damping, incorporating the action of external forces.Furthermore the evolution of the symplectic structure is analysed in thecontinuous and the discrete case. Existing methods are examined and novelmethods are designed using a lumped oscillator as an elemental model. Theproposed methodology is extended to the case of distributed systems andexemplified through a case study of a vibrating string bouncing against a rigidobstacle.

Structure preserving algorithms for simulation of linearly damped acoustic systems