Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach

Gross, B. J.; Trask, N.; Kuberry, P.; Atzberger, P. J.

doi:10.1016/j.jcp.2020.109340

Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach

Journal Article · 19 February 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109340· OSTI ID:1619207

Gross, B. J. ^[1]; Trask, N. ^[2]; ^[2]; ^[1]

Univ. of California, Santa Barbara, CA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of a system of second-order elliptic operators. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Univ. of California, Santa Barbara, CA (United States); University of California, Santa Barbara, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC04-94AL85000; SC0019246

OSTI ID:: 1619207

Alternate ID(s):: OSTI ID: 1602294
OSTI ID: 2331459
OSTI ID: 1633912

Report Number(s):: SAND--2019-5752J; 675748

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 409; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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