SUMMARYA new upwind finite element scheme for the incompressible Navier-Stokes equations at high Reynolds number is presented. The idea of the upwind technique is based on the choice of upwind and downwind points. This scheme can approximate the convection term to third-order accuracy when these points are located at suitable positions. From the practical viewpoint of computation, the algorithm of the pressure Poisson equation procedure is adopted in the framework of the finite element method. Numerical results of flow problems in a cavity and past a circular cylinder show excellent dependence of the solutions on the Reynolds number. The influence of rounding errors causing Karman vortex shedding is also discussed in the latter problem.
KEY WORDS Upwind finite element method Navier-Stokes equations Upwind and downwind points High-Reynolds-number flows Influence of rounding errors
Let n ≥ 1 be an integer and let 2 e be the highest power of 2 dividing n. For a prime number p = 2n + 1 with an odd prime number , let N be the imaginary abelian field of conductor p and degree 2 e+1 over Q. We show that for n ≤ 30, the relative class number h − N of N is odd when 2 is a primitive root modulo except for the case where (n,) = (27, 3) and p = 163 with the help of computer.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.