Elimination of delay-free loops in discrete-time models of nonlinear acoustic systems

Nonlinear acoustic systems are often described by means of nonlinear maps which act as instantaneous constraints on the solutions of a system of linear differential equations. This description leads to discrete-time models exhibiting non-computable loops. This paper presents a solution to this computability problem by means of geometrical transformation of the nonlinearities and algebraic transformation of the time-dependent equations. The proposed leads to stable and accurate simulations even at relatively low sampling rates.