Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method

Area of Science:

• Computational physics
• Acoustics
• Numerical analysis

Background:

• Acoustic wave propagation in attenuating media presents challenges for numerical methods.
• Existing methods often struggle with preserving both phase and amplitude accuracy, and capturing energy dissipation.
• Understanding and modeling these phenomena are crucial in various scientific and engineering fields.

Purpose of the Study:

• To develop a novel, stable, and efficient dissipation-preserving numerical method for acoustic wave propagation.
• To accurately model wave behavior in attenuating media, ensuring correct phase and amplitude.
• To reveal and preserve the intrinsic dissipation and conformal symplectic conservation laws.

Main Methods:

• Introduction of a conformal multi-symplectic structure to analyze the damped acoustic wave equation.
• Derivation of two subsystems: a conservative Hamiltonian wave equation and a dissipative linear ordinary differential equation (ODE) system.
• Construction of an explicit conformal symplectic scheme using the Strang splitting technique to combine solutions of the subsystems.

Main Results:

• The proposed method demonstrates stability and efficiency in preserving discrete versions of the conformal symplectic conservation law.
• Numerical tests show suppression of numerical dispersion and accurate preservation of energy dissipation in homogeneous media.
• The method effectively captures dissipation phenomena in heterogeneous media.

Conclusions:

• The novel conformal symplectic scheme offers a robust solution for acoustic wave propagation in attenuating media.
• It accurately preserves both phase and amplitude, and crucially, the energy dissipation.
• This method provides a significant advancement for simulating complex acoustic phenomena in diverse media.