Mesh-distortion threshold for numerical noise

Determine the level of hexahedral mesh distortion, quantified by the scaled Jacobian, that produces significant numerical noise in spectral-element simulations of coupled elastic-acoustic wave propagation.

Background

The spectral-element method represents the propagation medium using conformal hexahedral elements. Element distortion is measured by the scaled Jacobian, with values below 0.2 generally discouraged and values above 0.5 considered relatively safe. However, the paper notes that no rigorous criterion currently identifies the distortion level at which numerical noise becomes significant. This uncertainty motivates cross-validation between the spectral-element and pseudo-spectral solvers.

The problem concerns establishing a quantitative relationship between mesh geometry and numerical error, rather than merely reporting mesh-quality statistics for the dolphin-head model. A solution would provide principled guidance for constructing reliable hexahedral meshes for coupled elastic-acoustic simulations.