Affine particle in cell method for MAC grids and fluid simulation

•We propose an Affine-Particle-In-Cell transfer preserves linear and angular momentum.•Fourier analysis in 2D provides useful and intuitive information about the dissipation level of a particle-grid transfer.•The proposed Affine-Particle-In-Cell transfer shows low dissipation and it preserves vorticity well. We present a new technique for transferring momentum and velocity between particles and MAC grids based on the Affine-Particle-In-Cell (APIC) framework [1,2] previously developed for co-located grids. APIC represents particle velocities as locally affine, rather than locally constant as in traditional PIC. These previous APIC schemes were designed primarily as an improvement on Particle-in-Cell (PIC) transfers, which tend to be heavily dissipative, and as an alternative to Fluid Implicit Particle (FLIP) transfers, which tend to be noisy. The original APIC paper [1] proposed APIC-style transfers for MAC grids, based on a limit for multilinear interpolation. We extend these to the case of smooth basis functions and show that the proposed transfers satisfy all of the original APIC properties. In particular, we achieve conservation of angular momentum across our transfers, something which eluded [1]. Early indications in [1] suggested that APIC might be suitable for simulating high Reynolds fluids due to favorable retention of vortices, but these properties were not studied further and the question was left unresolved. One significant drawback of APIC relative to FLIP is that energy is dissipated even when Δt=0. We use two dimensional Fourier analysis to investigate dissipation in this important limit. We investigate dissipation and vortex retention numerically in the general case to quantify the effectiveness of APIC compared with PIC, FLIP, and XPIC.