Two-Dimensional Grid-Characteristic Schemes for Acoustic Wave Simulations

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 283 - 291
• Main Authors: Mi, X., Golubev, V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2025; Springer Nature B.V
• Subjects: Acoustic propagation; Acoustic waves; Algebra; Algorithms; Analysis; Approximation; Geometry; Mathematical analysis; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Numerical analysis; Probability Theory and Stochastic Processes; Splitting; Wave propagation; mathematical modeling; grid-characteristic method; operator splitting; acoustic media; seismic waves; 2010 Mathematics Subject Classification: 12345, 54321
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S199508022460852X

The paper is devoted to the numerical simulation of the acoustic wave propagation. A two-dimensional problem, typical for the seismic exploration process with the linear profiling is considered. A novel numerical algorithm is developed. It uses the operator splitting method to reduce an original multi-dimensional system of equations to the series of one-dimensional systems. Further, the grid-characteristic method is used to construct solutions of each one-dimensional hyperbolic problems. A distinctive feature of the developed algorithm is an application of a seven-point spatial stencil, which allows us to construct a fifth order one-dimensional scheme. The special multi-step operator splitting method is presented, that preserves an achieved approximation order in the final multi-dimensional scheme. The procedure of constructing consistent boundary and contact condition approximations is presented. Multiple test problems were successfully solved.