A characteristic/finite element algorithm for the 3-D Navier–Stokes equations using unstructured grids Original Research Article

This paper discusses a finite element algorithm for solution of the 3-D Navier–Stokes equations that is based on the method of characteristics. The algorithm which is based on a time-slitting of the convective terms from the generalized Stokes problem, comprises a point-wise characteristic integration of the 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. The implementation of the algorithm is discussed in the paper and the resulting codeʹs performance is compared to 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 over a backward-facing step, and flow in an end-to-side anastomoses. In all cases, the proposed algorithm demonstrated performance superior to that of a conventional explicit treatment of the convective terms.