Numerical Simulation Of The Problems In Fluid Mechanics Using Spectral/hp Element Method Based On Nektar++

Poisson equation and advection-diffusion equation are of great importance in fluid mechan-ics.Therefore,the research of these equations' numerical solution is of important theoretical and practical significance.In this paper,we use the spectral/hp element method based on ADRSolver in Nektar++ to analyse two dimensional Poisson equation,one-dimensional unsteady advection-diffusion equa-tions,two-dimensional unsteady and steady advection-diffusion equations in fluid mechanics,re-spectively,and we give out the error estimations of L2 and L? norm of u and the figures of the h-convergence and p-convergence of two kind of errors.The results show that:(1)The ADR-Solver in Nektar++ is suitable for these models,The numerical simulation results agree well with the analytical solutions.Furthermore,with the increasing of order p,the two kinds of norm er-rors decrease exponentially;(2)The Nektar++ software is effective for one dimensional unsteady advection-diffusion equations by comparing the results of Nektar++ with theoretical results and the results obtained by other numerical methods such as C-N scheme,EHOC scheme,high order compact difference scheme,and the accuracy of numerical solutions obtained is much higher in a certain range.