A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains
Abstract
A computationally efficient method for solving threedimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible NavierStokes equations on an unbounded staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation and incompressibility constraint are numerically solved by combining an integrating factor technique for the viscous term and a halfexplicit RungeKutta scheme for the convective term. A projection method that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rates, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. The accuracy and physical fidelity of solutions are verified through numerical simulations of vortex rings.
 Publication:

Journal of Computational Physics
 Pub Date:
 July 2016
 DOI:
 10.1016/j.jcp.2016.04.023
 arXiv:
 arXiv:1601.00035
 Bibcode:
 2016JCoPh.316..360L
 Keywords:

 Incompressible viscous flow;
 Unbounded domain;
 Lattice Green's function;
 Projection method;
 Integrating factor;
 Halfexplicit RungeKutta;
 Elliptic solver;
 Physics  Fluid Dynamics;
 Physics  Computational Physics
 EPrint:
 35 pages, 9 figures