Bottom Boundary-Fitted Free Surface Flow Simulation with Coordinate Transformation Using SPH(2)

Abstract

Particle methods such as the SPH and MPS methods have problems because it is difficult to treat curved bottom surfaces such as seabed surfaces accurately. In this study, regarding this problem, the curved bottom surfaces’ treatments have been improved using a coordinate transformation using the high-order second derivative model called SPH(2). Although the theory for the coordinate transformation was established in the MPS method, its accuracy did not give the desired accuracy because of the numerical errors of the second derivative models. Therefore, the numerical errors in these coordinate transformations were overcome by applying the second derivative model of SPH(2) to the coordinate transformation formulas. The superiority and validity of the proposed coordinate transformation using SPH(2) are demonstrated through validation examples such as the hydrostatic pressure and dam-break problems.