Cut Open The Operator Method For Solution Of Three-dimensional Viscous Flow Problems

On Three-Dimensional Numerical Solution of Incompressible Viscous Flow by OSFEM Abstract An algorithm for solution of three-dimensional Navier-Stokes equations for incompressible viscous flow is developed. A decoupled algorithm based on the operator-splitting technique is applied. The solution is obtained in subsequent stages treating equations split into parts having well-defined mathematical properties, so that the most adequate methods for a given differential operator type can be used. In the numerical solution algorithm, the method of characteristics, analytic method and Galerkin finite element method(Galerkin- FEM) can be chosen to solve the advective equation,diffusion equations, reaction(source/sink) equations, propagation equations and pressure Poisson equation, respectively. The developed new algorithm has been verified using analytical solution of circular conduit flow in a Reynolds number range of 100400. Meanwhile, this paper attempts to study on some important aspects of time- dependent incompressible viscous flow. Important missing aspects are: turbulent flow, numerical discretization techniques specially the relevant and difficult topic of numerical treatment of advection and related numerical methods of solution, variable property fluids, boundary layers, stability, etc. Rather, it focuses on more primitive and fundamental issues of numerical treatment of advective equation and proper formulation of initial boundary value(IB VP). Numerical problems associated with advective dominated transport include spurious oscillation, numerical dispersion, peak clipping, and grid oriention. However, the key of numerical solution of three-dimensional advective problem is searching for a high-precision interpolating function, which can keep the computational stability and low damping. For the pure 3D advective problem, solution can be found by the characteristics method. The solution algorithm involves tracing the characteristic lines backwards in time from a upwind element of an interior point. Two advanced mehtods, quasi-consistence and consistence hexahedral element method, for three-dimensional advective problem are developed. And comparison of these two methods with linear interpolating function method is implemented. The flow domain is discretized into arbitrary hexahedral elements. The verification of the algorithm is performed using a Gauss-distributed concentration ball and a stock wave at steady flow in an open channel. The comparison with an analytical problem solution shows that the precision and the stability of quasi-consistence hexahedral element method is as good as that of consistence hexahedral element method, better than that of the linear interpolating function method. For the variables with greater gradient, a high-precision interpolating function, such as quasi-consistence hexahedral element...