Title: An Embedded Boundary Integral Solver for the Unsteady Incompressible Navier-Stokes Equations 

(NYU-CS-TR838)

Authors: George Biros, Lexing Ying, and Denis Zorin 

Abstract:
We present a new method for the solution of the unsteady
incompressible Navier-Stokes equations. Our goal is to achieve a
robust and scalable methodology for two and three dimensional
incompressible laminar flows.  The Navier-Stokes operator
discretization is done using boundary integrals and structured-grid
finite elements. We use a two-step second-order accurate scheme to
advance the equations in time.  The convective term is discretized by
an explicit, but unconditionally stable, semi-Lagrangian formulation;
at each time step we inverta spatial constant-coefficient (modified)
Stokes operator.  The Dirichlet problem for the modified Stokes
operator is formulated as a double-layer boundary integral
equation. Domain integrals are computed via finite elements with
appropriate forcing singularities to account for the irregular
geometry. We use a velocity-pressure formulation which we discretize
with bilinear elements (Q1-Q1), which give equal order interpolation
for the velocities and pressures. Stabilization is used to circumvent
the div-stability condition for the pressure space. The integral
equations are discretized by Nystrom's method. For the specific
approximation choices the method is second order accurate. We will
present numerical results and discuss the performance and scalability
of the method in two dimensions.