A cylindrical axial-symmetric virtual element method for acoustic wave propagation
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In this presentation, we propose a Virtual Element Method for approximating the solution of the acoustic wave equation. A high-order approximation is crucial for obtaining reliable numerical solutions, along with the flexibility of using computational grids composed of cells with general shapes. Our main application is studying sound propagation in an acoustic horn and optimizing its shape by minimizing the input impedance at the throat of the horn. Given the geometry of the acoustic horn, we formulate the equations in axial-symmetric cylindrical coordinates and introduce an appropriate expansion in the numerical scheme to preserve high-order accuracy. This approach provides highly accurate solutions, which can serve as a forward model in the inversion algorithm for optimizing the horn geometry. We will present examples demonstrating the accuracy of the computed wave propagation and the method's effectiveness in achieving an optimal design.