An accurate and robust axisymmetric SPH method based on Riemann solver with applications in ocean engineering

The present work develops an accurate and robust axisymmetric SPH method by introducing the Riemann solver into the framework of axisymmetric SPH. To reduce numerical dissipations caused by the intrinsic numerical viscosity of the Riemann solver, PVRS Riemann solver with MUSCL reconstruction is embedded into the scheme of the axisymmetric Riemann SPH. In addition, in order to maintain the uniformity of particle distributions, the volume adaptive scheme and the particle shifting technique are applied in this work. The advantage of the present axisymmetric Riemann SPH method is that it can consider the real compressibility of the air, which allows a larger stable time step in the simulation of the strongly-compressible flows. Through the three benchmark tests, including the Sod shock tube test, the Sedov point explosion test and the blast wave problem test, the accuracy of the present axisymmetric Riemann SPH method is verified. Then this method is applied to the simulations of some practical issues in ocean engineering, including the shockwave propagation of the underwater explosion, the water entry of the sphere and the coalescence of an oscillating bubble pair.