Spectral element method for wave propagation on irregular domains

Abstract

A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss-Lobatto-Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are mapped according to the length scale of the beeline segment or the curve segment. Using the Bubnov-Galerkin method, some acoustic problems with two kinds of irregular domains are simulated in detail. First, the basic problem with analytical solution is analysed numerically. Numerical results show that the SEM integrated with the lengthscale method has the same precision as the isoparametric SEM. Also, it can save nearly half of the time cost. Additionally, the acoustic propagations with inlet flow are simulated numerically. All the results indicate that the SEM integrated with the length-scale method has the ability to simulate the acoustic problems with irregular domains. It is shown that the mapping method maintains the curve edges and provides a useful alternative for isoparametric element, which represents a curved edge with a straight edge.

An accurate triangular spectral element method-based numerical simulation for acoustic problems in complex geometries

“…In this way, SEM becomes an effective tool for CAA problems, with both high accuracy of traditional SEM and capable spatial discretization of different elements. In our previous work, 19 SEM with curved quadrilateral elements was carried out for wave propagation with an absorbing boundary condition (ABC). However, obvious distortion of wave can be observed near the artificial boundaries due to the accuracy inefficiency of ABC implemented.…”