Abstract:Numerical Methods for simulating fluid and its coupling to solid particles are essential tools in many fields of astronomy. In this talk, I will introduce a novel reconstruction scheme called the “piece-wise exponential method (PEM)”. It is 3rd order in space but uses only a 3-point stencil. Its simplicity is comparable to the popular piece-wise linear method, but is simultaneously less diffusive and less oscillatory. I will also introduce a novel particle integration scheme called the “staggered semi-analytic method (SSA)”, which is significantly more accurate and stable than the common implicit scheme in the strong drag limit (where the timestep is longer than the particle stopping time) and transitions naturally into a 2nd order symplectic scheme when the drag is weak. Finally, utilizing these innovations, I will present simulations that bring to light the ingredients necessary for planets to shepherd narrow rings in protoplanetary disks.
Advances in Gas and Dust Numerical Methods and Their Applications to Ring-Shepherding by Planets
Jeffrey Fung (IAS) // October 26, 2020
Abstract:Numerical Methods for simulating fluid and its coupling to solid particles are essential tools in many fields of astronomy. In this talk, I will introduce a novel reconstruction scheme called the “piece-wise exponential method (PEM)”. It is 3rd order in space but uses only a 3-point stencil. Its simplicity is comparable to the popular piece-wise linear method, but is simultaneously less diffusive and less oscillatory. I will also introduce a novel particle integration scheme called the “staggered semi-analytic method (SSA)”, which is significantly more accurate and stable than the common implicit scheme in the strong drag limit (where the timestep is longer than the particle stopping time) and transitions naturally into a 2nd order symplectic scheme when the drag is weak. Finally, utilizing these innovations, I will present simulations that bring to light the ingredients necessary for planets to shepherd narrow rings in protoplanetary disks.