Improved SPH method based on moving least square method for acoustic problems

Smoothed particle hydrodynamics is a widely used meshfree method. However, the order of the reproducing differential function is only the first order. To improve that, a corrective process termed as moving-least-square smoothed particle hydrodynamics, MLS-SPH, is introduced. Taylor expansion is used to modify the relation between arbitrarily distributed particles, and the concept of moving least square is used to approximate the value of the function and partial differential functions. This modified method can improve approximate accuracy effectively. Moreover, the order of approximate partial differential function becomes changeable, which expands the scope of its application. To investigate the advantages, a 2D complex surface approximation, a 2D model of Poisson problem with differential boundaries, and the acoustical modal of a rigid wall-bounded cavity are simulated.