Spline-Characteristic Method for Simulation of Convective Turbulence

Abstract

This paper describes the spline-characteristic method, an algorithm for direct numerical simulation of incompressible, thermal convection in which the method of characteristics has been combined with tricubic splines. The method of characteristics eliminates errors associated with large gradients of convected field and allows large time steps, and the splines provide an accurate spatial approximation. The proposed scheme is second-order in time and fourth-order in space. The applications of the spline-characteristic method to the vorticity-transport equation and to the Navier–Stokes equations in primitive variables in the framework of the projection method are discussed. This scheme can be efficiently parallelized and has been implemented on a distributed-memory, massively parallel computer, CM-5. The results are given for several test problems with different boundary conditions, both in 2D and 3D.