An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies

Gabbard, James; Gillis, Thomas; Chatelain, Philippe; van Rees, Wim M.

doi:10.1016/j.jcp.2022.111339

An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies

Journal Article · Wed Jun 01 00:00:00 EDT 2022 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2022.111339· OSTI ID:1870747

^[1]; Gillis, Thomas ^[2]; ^[3]; ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Massachusetts Institute of Technology
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Universite Catholique de Louvain, Louvain-la-Neuve (Belgium)

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by nonconvex immersed bodies, multiply connected domains, and the calculation of force distributions on immersed surfaces. The immersed interface method is re-interpreted as a polynomial extrapolation of flow quantities and boundary conditions into the immersed solid bodies, reducing computational cost and enabling simulations with nonconvex bodies that could not be discretized with previous immersed interface methods. In the flow, the vorticity transport equation is discretized using a conservative finite difference scheme and explicit Runge-Kutta time integration. The velocity reconstruction problem is transformed to a scalar Poisson equation that is discretized with conservative finite differences, and solved using an FFT-accelerated iterative algorithm. The use of conservative differencing throughout leads to exact enforcement of a discrete Kelvin's theorem, allowing for simulations with multiply connected domains and outflow boundaries that have challenged other immersed interface vortex methods. We also explore novel methods for recovering time-dependent pressure distributions on immersed bodies within a vorticity-based method and present a novel control volume formulation for recovering aerodynamic moments from only the vorticity and velocity fields. The method achieves second order spatial accuracy and third order temporal accuracy, and is validated on a variety of 2D flows in internal and free-space domains.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0020998

OSTI ID:: 1870747

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 464; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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