Abstract
A phase-space boundary integral method is developed for modelling stochastic high-frequency acoustic and vibrational energy transport in both single and multi-domain problems. The numerical implementation is carried out using the collocation method in both the position and momentum phase-space variables. One of the major developments of this work is the systematic convergence study, which demonstrates that the proposed numerical schemes exhibit convergence rates that could be expected from theoretical estimates under the right conditions. For the discretisation with respect to the momentum variable, we employ spectrally convergent basis approximations using both Legendre polynomials and Gaussian radial basis functions. The former have the advantage of being simpler to apply in general without the need for preconditioning techniques. The Gaussian basis is introduced with the aim of achieving more efficient computations in the weak noise case with near-deterministic dynamics. Numerical results for a series of coupled domain problems are presented, and demonstrate the potential for future applications to larger scale problems from industry.
Highlights
Noise and vibration simulations for mechanical structures are commonly performed using numerical solvers for linear wave equations [1,2]
We have presented a boundary integral model for the stochastic propagation of phase-space densities in both single and multi-domain problems
The collocation method has been applied in order to perform numerical experiments using piecewise constant basis functions in space and both Gaussian radial basis functions and Legendre polynomial basis functions in the direction variable
Summary
Noise and vibration simulations for mechanical structures are commonly performed using numerical solvers for linear wave equations [1,2]. Direct treatment of the Fokker–Planck equation is often considered infeasible [20], and in this work we will apply a boundary integral formulation of the Fokker–Planck equation for a Hamiltonian flow, where the associated boundary integral operator will take the form of a stochastic evolution operator Through this approach we achieve a reduction in dimensionality to the boundary phase-space, which makes the corresponding numerical models both smaller and simpler to implement. Despite requiring additional preconditioning strategies in order to obtain convergence, the latter has the advantage of providing an exact representation of the typical initial conditions in our proposed model and has the potential for computational cost savings in the case of near-deterministic propagation These phase-space collocation schemes are detailed throughout Sect. We detail a series of numerical experiments for multi-domain problems in Sect. 5, demonstrating the potential of the proposed methods to model built up structures from industrial applications in high-frequency structural vibrations and acoustics
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
