Three-Temperature Boundary Element Modeling of Ultrasound Wave Propagation in Anisotropic Viscoelastic Porous Media

• Published in: Axioms Vol. 12; no. 5; p. 473
• Main Authors: Fahmy, Mohamed Abdelsabour, Alsulami, Mohammed O., Abouelregal, Ahmed E.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.05.2023
• Subjects: anisotropic viscoelastic porous media; Anisotropy; Boundary element method; Boundary element methods; boundary element model; Boundary integral method; Engineering; Finite difference method; Integral equations; Mathematical models; Nonlinearity; Numerical analysis; Porous materials; Porous media; Propagation; Radiation; Stress waves; Temperature; three-temperature; ultrasonic wave propagation; Ultrasonic waves; Viscoelasticity; Wave propagation; Saudi Arabia
• ISSN: 2075-1680; 2075-1680
• DOI: 10.3390/axioms12050473

The main goal of this work is to develop a novel boundary element method (BEM) model for analyzing ultrasonic wave propagation in three-temperature anisotropic viscoelastic porous media. Due to the problems of the strong nonlinearity of ultrasonic wave propagation in three-temperature porous media, the analytical or numerical solutions to the problems under consideration are always challenging, necessitating the development of new computational techniques. As a result, we use a new BEM model to solve such problems. A time-stepping procedure based on the linear multistep method is obtained after solving the discretized boundary integral equation with the quadrature rule. The calculation of a double integral is required to obtain fundamental solutions, but this increases the total BEM computation time. Our proposed BEM technique is used to solve the current problem and improve the formulation efficiency. The numerical results are graphed to demonstrate the effects of viscosity and anisotropy on the nonlinear ultrasonic stress waves in three-temperature porous media. The validity, accuracy, and efficiency of the proposed methodology are demonstrated by comparing the obtained results to a corresponding solution obtained from the finite difference method (FDM).