High-order X-FEM for the simulation of sound absorbing poro-elastic materials with coupling interfaces

Abstract In this paper, the acoustic field with the presence of poro-elastic materials is simulated by the eXtended Finite Element Method (X-FEM). Problems involving interfaces between different media are our main focus. The proposed method allows interfaces to be embedded in the finite elements, easing significantly the discretization, especially when the geometry of the interface is complex. The gradient discontinuity at the interface is handled through the ridge enrichment function. The strategies of spatial discretization for two different types of coupling interface are provided. A high-order approximation is used to improve the rate of convergence for the Biot mixed formulation ( u s , p ) and to eliminate the pollution effect at high frequencies. The verification of the method is performed with two benchmarks. Convergences of the solutions exhibit the capability and the accuracy of the present method under different conditions: coupling types, geometric complexity and a wide range of frequency. The applicability and advantage of the method in practical situations are demonstrated by a car cavity problem where part of the geometry is modified without re-meshing. This paper demonstrates that high-order X-FEM is an efficient computational approach for analysing sound-absorbing poro-elastic materials involving complex geometries.

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