Fig. 1. Ink drop. We compare from left to right FLIP, APIC, and PolyPIC for an inkjet in an ambient incompressible fluid. PolyPIC more effectively resolves the vorticial details.Recently the Affine Particle-In-Cell (APIC) Method was proposed by 2017b] to improve the accuracy of the transfers in Particle-In-Cell (PIC) [Harlow 1964] techniques by augmenting each particle with a locally affine, rather than locally constant description of the velocity. This reduced the dissipation of the original PIC without suffering from the noise present in the historic alternative, Fluid-Implicit-Particle (FLIP) [Brackbill and Ruppel 1986]. We present a generalization of APIC by augmenting each particle with a more general local function. By viewing the grid-to-particle transfer as a linear and angular momentum conserving projection of the particle-wise local grid velocities onto a reduced basis, we greatly improve the energy and vorticity conservation over the original APIC. Furthermore, we show that the cost of the generalized projection is negligible over APIC when using a particular class of local polynomial functions. Lastly, we note that our method retains the filtering property of APIC and PIC and thus has similar robustness to noise.
Favipiravir was first synthesized from an inexpensive and commercially available starting material, 2-aminopyrazine. The preferred route embedded within Scheme 4 consisted of seven steps, and was highlighted by the novel and efficient synthesis of 3,6-dichloropyrazine-2-carbonitrile 8. This intermediate was prepared in four successive steps which were regioselective chlorination of the pyrazine ring, bromination, Pd-catalyzed cyanation, and Sandmeyer diazotization/chlorination. This protocol eliminated the hazardous POCl 3 of previous synthetic methods and offered a better yield (48%) which was 1.3-fold higher than a recently published procedure. From intermediate 8, the subsequent nucleophilic fluorination, nitrile hydration and hydroxyl substitution efficiently afforded the target product. Another synthetic approach with the same starting material was also investigated to bypass the allergy-causing dichloro intermediate 8. However, the key step of monofluorination at the pyrazine C6 position of intermediate 19 or 22 was not achieved.
In this paper, we present a mixed explicit and semi-implicit Material Point Method for simulating particle-laden flows. We develop a Multigrid Preconditioned fluid solver for the Locally Averaged Navier Stokes equation. This is discretized purely on a semi-staggered standard MPM grid. Sedimentation is modeled with the Drucker-Prager elastoplasticity flow rule, enhanced by a novel particle density estimation method for converting particles between representations of either continuum or discrete points. Fluid and sediment are two-way coupled through a momentum exchange force that can be easily resolved with two MPM background grids. We present various results to demonstrate the efficacy of our method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with đź’™ for researchers
Part of the Research Solutions Family.