A characteristic/finite element algorithm for the 3-D Navier-Stokes equations using unstructured grids (Q1976152)

This paper discusses a finite element algorithm for solution of three-dimensional Navier-Stokes equations that is based on the method of characteristics. The algorithm which employs a time-slitting of convective terms form the generalized Stokes problem, comprises a point-wise characteristic integration of convective terms, and Uzawa integration of the generalized Stokes problem. The most costly part of the characteristic integration scheme is the search for an element containing the foot of a given characteristic. The present study uses a very efficient algorithm for element searching, which is particularly useful for complex geometries. We discuss the implementation of the algorithm, and compare the resulting code's performance with that of a code based on a more conventional, fourth-order Runge-Kutta convection integration. A variety of flow problems are tested, including an analytical solution of the Navier-Stokes equations, flow in a lid-driven cavity flow, flow over a backward-facing step, and flow in an end-to-side anastomosis. In all cases, the proposed algorithm demonstrates peformance superior to that of a conventional explicit treatment of convective terms.