Oral Presentation

A Numerical Scheme Ensuring Total Energy Conservation Including Self-Gravity

Author(s): Tomoyuki Hanawa (Chiba U.)

Presenter: Tomoyuki Hanawa (Chiba University)

Total energy of an astronomical system is of our great interest, since the evolution of the system depends on it. Hence we solve the hydrodynamical equations taking account of the conservation in our simulations. However, gravitational energy is often taken into account as a source term and the total energy including gravity is not guaranteed. This is partly because it takes additional computational cost to solve hydrodynamical equations in the fully conservative form. This paper shows that the conservation of total energy is ensured if the source term due to gravity is properly taken into account. The gravity is defied not at cell center but on cell surface in this method. This method ensures also the conservation of total momentum. The method is developed for a self-gravitating system but can be applied to the case where the gravitational force is given explicitly as a function. A numerical example demonstrate that change in the total energy is as small as round-off error in numerical simulations of Jeans instability. This method gives a constraint on discretization of the Poisson equation on a octree mesh often used in adaptive mesh refinement (AMR). Otherwise, total energy conservation is violated.