BOTTOM BOUNDARY-FITTED PARTICLE METHOD WITH COORDINATE TRANSFORMATION USING SPH(2) WITH SPATIAL 2ND-ORDER ACCURACY

Abstract

Particle methods such as the SPH and MPS methods have problems in that the approximation accuracy decreases due to disorder in particle arrangements and it is difficult to treat accurately curved bottom surfaces such as seabed surface. Regarding the first problem, we proposed the SPH(2), which satisfy the second order convergence in space and maintain its accuracy against for particle disorders. In this study, the second problem, the treatments of the curved bottom surfaces, has been improved using a coordinate transformation with the SPH(2)'s second derivative model 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 hydrostatic pressure problems and dam breakage problems.