Abstract
We propose the use of PolyPIC transfers [10] to construct a second order accurate discretization of the Navier-Stokes equations within a particle-in-cell framework on MAC grids. We investigate the accuracy of both APIC [16,17,8] and quadratic PolyPIC [10] transfers and demonstrate that they are suitable for constructing schemes converging with orders of approximately 1.5 and 2.5 respectively. We combine PolyPIC transfers with BDF-2 time integration and a splitting scheme for pressure and viscosity and demonstrate that the resulting scheme is second order accurate. Prior high order particle-in-cell schemes interpolate accelerations (not velocities) from the grid to particles and rely on moving least squares to transfer particle velocities to the computational grid. The proposed method instead transfers velocities to particles, which avoids the accumulation of noise on particle velocities but requires the polynomial reconstruction to be performed using polynomials that are one degree higher. Since this polynomial reconstruction occurs over the regular grid (rather than irregularly distributed particles), the resulting weighted least squares problem has a fixed sparse structure, can be solved efficiently in closed form, and is independent of particle coverage.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.