TY - JOUR
T1 - A new mixed potential representation for unsteady, incompressible flow
AU - Greengard, Leslie
AU - Jiang, Shidong
N1 - Funding Information:
The work of the second author was supported in part by the NSF under grant DMS-1720405 and by the Flatiron Institute, a division of the Simons Foundation.
Funding Information:
∗Received by the editors September 24, 2018; accepted for publication (in revised form) February 4, 2019; published electronically November 6, 2019. https://doi.org/10.1137/18M1216158 Funding: The work of the second author was supported in part by the NSF under grant DMS-1720405 and by the Flatiron Institute, a division of the Simons Foundation. †Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, and Flatiron Institute, Simons Foundation, New York, NY 10010 ([email protected]). ‡Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102 ([email protected]).
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics.
PY - 2019
Y1 - 2019
N2 - We present a new integral representation for the unsteady, incompressible Stokes or Navier-Stokes equations, based on a linear combination of heat and harmonic potentials. For velocity boundary conditions, this leads to a coupled system of integral equations: one for the normal component of velocity and one for the tangential components. Each individual equation is well-conditioned, and we show that using them in predictor-corrector fashion, combined with spectral deferred correction, leads to high-order accuracy solvers. The fundamental unknowns in the mixed potential representation are densities supported on the boundary of the domain. We refer to one as the vortex source, the other as the pressure source, and to the coupled system as the combined source integral equation.
AB - We present a new integral representation for the unsteady, incompressible Stokes or Navier-Stokes equations, based on a linear combination of heat and harmonic potentials. For velocity boundary conditions, this leads to a coupled system of integral equations: one for the normal component of velocity and one for the tangential components. Each individual equation is well-conditioned, and we show that using them in predictor-corrector fashion, combined with spectral deferred correction, leads to high-order accuracy solvers. The fundamental unknowns in the mixed potential representation are densities supported on the boundary of the domain. We refer to one as the vortex source, the other as the pressure source, and to the coupled system as the combined source integral equation.
KW - Boundary integral equations
KW - Harmonic potentials
KW - Heat potentials
KW - Mixed potential formulation
KW - Navier-Stokes equations
KW - Predictor-corrector method
KW - Spectral deferred correction method
KW - Unsteady Stokes ow
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U2 - 10.1137/18M1216158
DO - 10.1137/18M1216158
M3 - Review article
AN - SCOPUS:85077993907
SN - 0036-1445
VL - 61
SP - 733
EP - 755
JO - SIAM Review
JF - SIAM Review
IS - 4
ER -