A compact three‐dimensional fourth‐order scheme for elasticity using the first‐order formulation. (29th July 2021)

• Record Type: Journal Article
• Authors: Gordon, Rachel; Turkel, Eli; Gordon, Dan
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 21(2021)
• Page Start: 6341
• Page End: 6360
• Publication Date: 2021-07-29
• Subjects: compact schemes -- elastic wave equation -- first‐order formulation -- fourth‐order accuracy -- frequency space -- staggered grid; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6794
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: We develop a compact fourth‐order scheme for the three‐dimensional elastic wave equation in frequency space, using the first‐order velocity‐stress formulation. The scheme is implemented numerically for homogeneous media on a staggered grid, and both the acoustic and elastic cases are considered. We use a one‐directional point source of impact, for which Pilant developed a closed solution. Numerical results for the acoustic and the elastic cases compare favorably with the analytic solutions and show a very significant improvement over the second‐order scheme.