![]() ![]() (SNL-NM), Albuquerque, NM (United States) Univ. Publication Date: Wed Feb 19 00:00: Research Org.: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States) of California, Santa Barbara, CA (United States) The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. 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. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. ![]()
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