Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Asymptotic transmission of solitons through random media
SIAM Journal on Applied Mathematics
Wave field simulation for heterogeneous porous media with singular memory drag force
Journal of Computational Physics
Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme
Computers & Mathematics with Applications
Efficient solution of a wave equation with fractional-order dissipative terms
Journal of Computational and Applied Mathematics
Biot-JKD model: Simulation of 1D transient poroelastic waves with fractional derivatives
Journal of Computational Physics
| Hi-index | 31.45 |
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a nonlinear PDE describing nonlinear acoustic waves, and a linear ODE describing the oscillations in the Helmholtz resonators. The thermal and viscous losses in the tube and in the necks of the resonators are modeled by fractional derivatives. A diffusive representation is followed: the convolution kernels are replaced by a finite number of memory variables that satisfy local ordinary differential equations. A splitting method is then applied to the evolution equations: their propagative part is solved using a standard TVD scheme for hyperbolic equations, whereas their diffusive part is solved exactly. Various strategies are examined to compute the coefficients of the diffusive representation; finally, an optimization method is preferred to the usual quadrature rules. The numerical model is validated by comparisons with exact solutions. The properties of the full nonlinear solutions are investigated numerically. In particular, the existence of acoustic solitary waves is confirmed.