Digital waveguide modeling for wind instruments: building a state-space representation based on the Webster-Lokshin model

This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations for the refined acoustic model of Webster-Lokshin. This acoustic model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar or spherical waves. Moreover, three types of discontinuities of the shape can be taken into account (radius, slope and curvature). The purpose of this work is to build low-cost digital simulations in the time domain based on the Webster-Lokshin model. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to a Kelly-Lochbaum network of input/output systems and delays. Second, for a systematic assembling of elements, their state-space representations are derived in discrete time. Then, standard tools of automatic control are used to reduce the complexity of digital simulations in the time domain. The method is applied to a real trombone, and results of simulations are presented and compared with measurements. This method seems to be a promising approach in term of modularity, complexity of calculation and accuracy, for any acoustic resonators based on tubes

Three-Dimensional Network Model for Coupling~of~Fracture and Mass Transport in Quasi-Brittle Geomaterials

Dual three-dimensional networks of structural and transport elements were combined to model the effect of fracture on mass transport in quasi-brittle geomaterials. Element connectivity of the structural network, representing elasticity and fracture, was defined by the Delaunay tessellation of a random set of points. The connectivity of transport elements within the transport network was defined by the Voronoi tessellation of the same set of points. A new discretisation strategy for domain boundaries was developed to apply boundary conditions for the coupled analyses. The properties of transport elements were chosen to evolve with the crack opening values of neighbouring structural elements. Through benchmark comparisons involving non-stationary transport and fracture, the proposed dual network approach was shown to be objective with respect to element size and orientation

A new continuous-discontinuous damage model: cohesive cracks via an accurate energy-transfer process

A new continuous-discontinuous strategy to describe failure of quasi-brittle materials is presented. For the early stages of the failure process, a gradient-enhanced model based on smoothed displacements is employed. As soon as the damage parameter exceeds a critical value Dcrit<1, a cohesive crack is introduced. A new criterion to estimate the energy not yet dissipated by the bulk when switching models-from continuous to continuous-discontinuous-is proposed. Then, this energy is transferred to the cohesive crack thus ensuring that the continuous and the continuous-discontinuous strategies are energetically equivalent. Compared to other existing techniques, this new strategy accounts for the different unloading branches of damage models and thus, a more accurate estimation of the energy that has to be transferred is obtained. The performance of this technique is illustrated with one- and two-dimensional examples.Peer ReviewedPostprint (author’s final draft

Flood propagation modelling with the Local Inertia Approximation: theoretical and numerical analysis of its physical limitations

Attention of the researchers has increased towards a simplification of the complete Shallow water Equations called the Local Inertia Approximation (LInA), which is obtained by neglecting the advection term in the momentum conservation equation. In the present paper it is demonstrated that a shock is always developed at moving wetting-drying frontiers, and this justifies the study of the Riemann problem on even and uneven beds. In particular, the general exact solution for the Riemann problem on horizontal frictionless bed is given, together with the exact solution of the non-breaking wave propagating on horizontal bed with friction, while some example solution is given for the Riemann problem on discontinuous bed. From this analysis, it follows that drying of the wet bed is forbidden in the LInA model, and that there are initial conditions for which the Riemann problem has no solution on smoothly varying bed. In addition, propagation of the flood on discontinuous sloping bed is impossible if the bed drops height have the same order of magnitude of the moving-frontier shock height. Finally, it is found that the conservation of the mechanical energy is violated. It is evident that all these findings pose a severe limit to the application of the model. The numerical analysis has proven that LInA numerical models may produce numerical solutions, which are unreliable because of mere algorithmic nature, also in the case that the LInA mathematical solutions do not exist. The applicability limits of the LInA model are discouragingly severe, even if the bed elevation varies continuously. More important, the non-existence of the LInA solution in the case of discontinuous topography and the non-existence of receding fronts radically question the viability of the LInA model in realistic cases. It is evident that classic SWE models should be preferred in the majority of the practical applications

Evaluating the effect of scale and heterogeneity on the mechanical behaviour of rock blocks

Rock block strength is a significant factor controlling the rock mass behaviour and the rock-support interactions in fractured rock masses. Especially when the design relies on discontinuum analysis, the adopted block properties are a dominant driver influencing the results. A series of 2D UDEC grain-based models were performed on samples of different sizes and qualities to simulate the results of lab- and block-scale experiments. The effect of pre-existing defects was simulated either in a smeared sense by adjusting the grain micro-properties or by explicitly modelling micro-Discrete Fracture Networks (DFN) that were previously generated within FracMan. Relationships that link the rock block strength with its volume and in-situ heterogeneity were proposed for the estimation of scaled Mohr–Coulomb and Hoek–Brown parameters. The UCS of blocks was expressed as a function of scale, defect intensity, persistence and strength. The quantified scale/condition dependant reduction of block strength was then linked with a block-scale Geological Strength Index parameter named micro GSI (mGSI). Special focus was also given on the selection of appropriate constitutive relationships and discontinuum modelling techniques when simulating tunnel-scale problems. For continuum blocks in-between DFNs the traditional Hoek–Brown approach does not capture realistic behaviours and the modified Damage-Initiation and Spalling-Limit approach is needed to predict the expected damage near the excavation boundaries. When blocks are simulated as a packing of grain elements, considerably reduced damage, stress relaxation and deformation is predicted as the Voronoi skeleton creates a well-interlocked structure that clamps the pre-existing joints. The research highlights that the estimation of representative block properties is of equivalent importance with the selection of appropriate modelling approaches

Discontinuities in numerical radiative transfer

Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of the stationary radiative transfer equation is particularly challenging in such situations, because standard numerical methods may perform very inefficiently in the absence of local smoothness. However, a rigorous investigation of the numerical treatment of the radiative transfer equation in discontinuous media is still lacking. The aim of this work is to expose the limitations of standard convergence analyses for this problem and to identify the relevant issues. Moreover, specific numerical tests are performed. These show that discontinuities in the atmospheric physical parameters effectively induce first-order discontinuities in the radiative transfer equation, reducing the accuracy of the solution and thwarting high-order convergence. In addition, a survey of the existing numerical schemes for discontinuous ordinary differential systems and interpolation techniques for discontinuous discrete data is given, evaluating their applicability to the radiative transfer problem

Synthetic models for the analysis and control of composite and sandwich aerospace structures in critical conditions

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