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.