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Multi-resolution lattice Green's function method for incompressible flows

Yu, Ke and Dorschner, Benedikt and Colonius, Tim (2020) Multi-resolution lattice Green's function method for incompressible flows. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20201118-081244277

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Abstract

We propose a multi-resolution strategy that is compatible with the lattice Green's function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2010.13213arXivDiscussion Paper
ORCID:
AuthorORCID
Yu, Ke0000-0003-0157-4471
Dorschner, Benedikt0000-0001-8926-7542
Colonius, Tim0000-0003-0326-3909
Additional Information:This work was supported by the ONR grant No. N00014-16-1-2734, the AFOSR/UCLA grant No. FA9550-18-1-0440 and the SNF Grant No. P2EZP2 178436 (B. D.). This work used the Extreme Science and Engineering Discovery Environment [37], which is supported by National Science Foundation grant number ACI-1548562. Specifically, the computations presented here used Comet at the San Diego Supercomputer Center and Stampede 2 at the Texas Advanced Computing Center through allocation TG-CTS120005.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-16-1-2734
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0440
Swiss National Science Foundation (SNSF)P2EZP2_178436
NSFACI-1548562
NSFTG-CTS120005
Subject Keywords:Lattice Green’s function; Multi-resolution; Adaptive mesh refinement; Finite-volume; Vortex rings
Record Number:CaltechAUTHORS:20201118-081244277
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201118-081244277
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106718
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Nov 2020 18:28
Last Modified:18 Nov 2020 18:28

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