Absorbing boundary conditions for the Westervelt equation
This work provides more accurate boundary conditions for nonlinear wave propagation problems, benefiting computational acoustics and related fields.
The authors constructed a family of nonlinear absorbing boundary conditions for the Westervelt equation in 1D and 2D using pseudo-differential calculus, achieving high-order accuracy. Numerical experiments demonstrated efficiency across different wave propagation regimes.
The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation.