Spectral Element Methods for Transient Acoustics in ANSYS LS-DYNA®

Increasingly there is an emphasis in the engineering simulation community on ultrasonic devices. They are seen in medical imaging, structural health monitoring, and of course, in the rapidly emerging world of autonomous/semi-autonomous vehicles. These devices operate at frequencies of 50KHz and above, sometimes well above. Wavelengths at those frequencies are measured in millimeters, sometimes even micrometers. The simulation of the propagation of such short waves over any substantial distance is a very demanding endeavor. This is especially true if tri-linear/quadratic iso-parametric finite elements are used. Newer, higher-order finite element methods exist [1]. Among those methods is the spectral element method (SEM). Many SEM references are available in the literature, a sampling being [1-6.] Spectral elements are appealing because they are highly accurate and can be efficiently incorporated in an explicit solver like LS-DYNA. In a massively parallel setting, they allow for the solution of models with billions of degrees-of-freedom in a reasonable amount of time.