A Parallel Stabilization Method For3D Navier-Stokes Equations

Navier-Stokes equations are the class of nonlinear equations in fluidmechanics, appeared in many fields of theory and application research. Theresearch is important for people to understand and master the fluid mo-tion law. Based on the the fact that the understanding of this nonlinearphenomenon is limited, the numerical simulation has become an importantmeasure of study. But, the difculty on the numerical simulation of theNavier-Stokes equations is large scale and the contradiction between longtime integral arithmetic and the limited computational resources. There-fore, in order to implement the large scale numerical simulation of theNavier-Stokes equations and deepen the understanding of the law of fluidmotion, the parallel computing technology is needed.Based on two local Gauss integration variational multiscale algorithm,a parallel Newton-linearized finite element algorithm for the3D Navier-St-okes equations is proposed and analyzed. In this algorithm a nonlinearproblem on a coarse grid is first solved by Newton iterative method, andthen correction are calculation by solving a linearized Newton problem inparallel on overlapped fine grid subdomains. By using local a priori errorestimate for the finite element solution and under the strong uniquenesscondition, error bounds of the corresponding finite element solution areanalyzed. Numerical results are also given to demonstrate the efectivenessof the algorithm.