###### Abstract  
This paper presents a modified time discontinuous Galerkin finite element method (MDGFEM) for transient acoustic wave propagation problem of multilayered pavement. The pavement consists of cement concrete pavement, semi-rigid base, and natural soil. The multilayered pavement is modeled as poroelastic mediums and assumed to be water-saturated. The well-known generalized Biot's theory is employed to describe the wave propagation problem. The present MDGFEM, based on the artificial damping scheme, employs the Hermite (P3) functions and the linear (P1) shape functions to interpolate the global nodal vector and its temporal gradient respectively in a time step. Numerical results of 1D and 2D problems show that the MDGFEM can filter out spurious numerical oscillations before and after waves, boundaries of the hole, and the interface between the layers more effectively for the propagation of acoustic waves in multilayered pavement. Compared with widely used time-continuous methods such as the Newmark method, the method proposed in this paper presents better capabilities in the fluid-structure interaction behavior of multilayer pavements and provides a more accurate solution, which contributes to the further development of non-destructive testing of multilayer pavement structures.  
B +
Footnote †: journal: Applied Sciences  
_Applied_  
_Acticle_  
**Transient Acoustic Wave Propagation Problems in Multilayered Pavement Using a Time Discontinuous Galerkin Finite Element Method**  
**J.-P.-M.-M.  
representation of acoustic propagation in multilayer pavement with irregular interfaces is challenging, and simulation of this problem is also a motivation for our study. The time domain and space domain of sound wave propagation in multilayer pavement are discontinuous, which makes the traditional time continuous method no longer applicable.  
In the traditional time-continuous Galerkin method represented by the Newmark method, time discontinuity is not allowed. In its general implementation, the discontinuity exists in the time domain, the space domain is not described accurately, and spurious numerical oscillations always appear in the wave-after stage. In the time discontinuous Galerkin finite element scheme, the time interval is further subdivided into independent time plates and time discontinuities between plates are allowed [11]. It has been shown that time discontinuous Galerkin finite element schemes have superior stability, robustness, and higher-order accuracy, and the schemes have evolved considerably in the last decades [12]. However, high-order discontinuous Galerkin methods always have high order polynomials inside each mesh element and high cost per iteration. [PERSON] et al. presented a novel time-discontinuous Galerkin finite element method [13,14], which has lower order polynomials and lower cost, for solving wave propagation problems with weak numerical oscillations generated at the interfaces between different layers. Based on the above studies, we propose an improved time-discontinuous Galerkin finite element method for simulating fluid-structure coupled problems, using an artificial damping scheme to reduce the numerical oscillations occurring at the wavefront and interlayer interfaces, with a particular focus on the solution of the impact problem of multi-layer saturated pavements [15,16].  
In this work, we describe the acoustic wave propagation problem of multilayered pavement of water saturated by using the generalized Biot's theory and extending the new version numerical algorithm to solve the equations. The results of three examples show that the present MDGFEM can effectively filter out the spurious numerical oscillations generated at the wave-front stage and interfaces between pavement layers. MDGFEM provides a more accurate solution than CGFEM (such as the Newmark method) under the premise of using the same time step size for the acoustic wave propagation problem of multilayered pavement of water saturated and subjected to impulsive loading.