Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme
Computers & Mathematics with Applications
Existence results for an evolution problem with fractional nonlocal conditions
Computers & Mathematics with Applications
Time domain numerical modeling of wave propagation in 2D heterogeneous porous media
Journal of Computational Physics
Biot-JKD model: Simulation of 1D transient poroelastic waves with fractional derivatives
Journal of Computational Physics
Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators
Journal of Computational Physics
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We consider a wave equation with fractional-order dissipative terms modeling visco-thermal losses on the lateral walls of a duct, namely the Webster-Lokshin model. Diffusive representations of fractional derivatives are used, first to prove existence and uniqueness results, then to design a numerical scheme which avoids the storage of the entire history of past data. Two schemes are proposed depending on the choice of a quadrature rule in the Laplace domain. The first one mimics the continuous energy balance but suffers from a loss of accuracy in long time simulation. The second one provides uniform control of the accuracy. However, even though the latter is more efficient and numerically stable under the standard CFL condition, no discrete energy balance has been yet found for it. Numerical results of comparisons with a closed-form solution are provided.