An Improved Multipole Approximation for Self-Gravity and Its Importance for Core-Collapse Supernova Simulations

Understand

Self-gravity computation by multipole expansion is a common approach in problems such as core-collapse and Type Ia supernovae, where single large condensations of mass must be treated.

• The standard formulation of multipole self-gravity suffers from two significant sources of error, which we correct in the formulation presented in this article.
• The first source of error is due to the numerical approximation that effectively places grid cell mass at the central point of the cell, then computes the gravitational potential at that point, resulting in a convergence failure of the multipole expansion.
• We describe a new scheme that avoids this problem by computing gravitational potential at cell faces.