Boundary integral/spectral element approaches to the Navier‐Stokes equations

Numerical algorithms are presented which combine spectral expansions on elemental subdomains with boundary integral formulations for solving viscous flow problems. Three distinct algorithms are described. The first demonstrates the use of spectral elements for the classic boundary integral method for steady Stokes flow. The second extends this algorithm to include domain integrals for solution of the unsteady Navier‐Stokes equations. The third algorithm explores the use of boundary integrals as a means of consolidating uncoupled elemental solutions in a domain decomposition approach. Numerical results demonstrating high‐order convergence are presented in each case.