A Lagrangian approach for computational acoustics with particle-based method

Abstract

Although Eulerian approaches are standard in computational acoustics, they are less effective for problems with moving boundaries and multiphase systems like bubble acoustics. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically with particle-based methods. Fluid dynamic equations is divided into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, the smoothed particle hydrodynamics (SPH) method and the corrective smoothed particle (CSP) method are introduced to solve the perturbation equations in Lagrangian form. A hybrid meshfree and finite-difference time-domain boundary treatment technique is utilized to represent acoustic boundaries. Finally, applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP method exhibits accuracy convergence in cases with different background flow. Different acoustic boundary conditions are validated as being effective for benchmark problems in computational acoustics.