| Abstract |
Particle methods for fluid simulations, such as the Smoothed Particle Dynamics, have been applied to a variety of problems in astrophysics and planetary science.
However, there are problems to which the application of particle methods has been considered difficult. Moreover, recently numerical problems have been found in simulations with standard formulation of SPH. In this talks, as an example of the former problems, We discuss the mantle convection. Historically, the combination of the unelastic approximation, the neglect of the inertia term, and the extended Boussinesq approximation has been used. This combination is necessary since the speed of the mantle convection is smaller than the sound speed by more than ten orders of magnitude. We propose a method to increase the inertia term, instead of neglecting it, thereby reducing both the sound speed and effective viscosity. By this transformation, it becomes possible to apply simple explicit method to mantle convection. For the latter problem, we first show numerical examples and then fundamental problems in the current formulation of SPH (and other particle methods), and discuss possible solutions. |
