Non-linear evolution of a sinusoidal pulse under a Brinkman-based poroacoustic model

• Darcy term acts as a dampening term for the wave equation.
• Brinkman term transforms the nature of the equation from hyperbolic to diffusive.
• Non-linear term induces finite time blow-ups.
• Darcy and Brinkman terms (in the hyperbolic regime) mitigate blow-ups.
• Strong Brinkman term (low Reynolds number) forbids blow-ups.

Through numerical analyses, we study the roles of Brinkman viscosity, the Darcy coefficient, and the coefficient of non-linearity on the evolution of finite amplitude harmonic waves. An investigation of acoustic blow-ups is conducted, showing that an increase in the magnitude of the non-linear term gives rise to blow-ups, while an increase in the strength of the Darcy and/or Brinkman terms mitigate them. Finally, an analytical study via a regular perturbation expansion is given to support the numerical results.