To Solve The Fluid Dynamics Problems By Finite Element Method

The finite element method is a common numerical simulation method to solve by drodynamics problems.Compared to the finite difference method and the finite integra 1 method,the finite element method is more efficient under complicated boundary situ ations.What's more,it can improve the precision in partial solution domain.The cor e idea of finite element method is to yield approximate values of the unknows at d iscrete number of points over the continuous domain and then approximate a solutio n by minimizing an associated error against the real solution through the interpolatio n function at discrete units.Application of two common finite element methods,the G akerkin method and the least-squares finite element method,to solve simple hydrodyn amic problems are mainly studied in this artical.Based on the research of two-dimension unsteady Navier-Stokes equations contr olled by a grooving slab dragging model,after discretizing the equations through Gak erkin method the solution in discrete domain are to be got,which indicates how the gr oove flows work in the process of acceleration and deceleration of the slab.Why flow s do not stop at the moment the slab stops being dragged in the premise of ignoring th e inertia item in the governing equation and how the flows stream in every second dur ing the dragging of the slab are analyzed in detail in this artical,which show that Gak erkin method works well in solving simple hydrodynamic problems and getting a idea 1 outcome.A large problem of multi-grids can be solved by least-square finite element meth od based on the research of three-dimension steady Navier-Stokes equations controlle d by a cavity flow model.Turning the governing equation into a first-order partial diff erential system and making a discretization by the Least-squares finite element method,the discrete matrix equations are then formed and solved and thus how the flu id in the cavity flow changes can be figured out.How the cavity flow works under dif ferent Reynolds numbers are to be analyzed,which demonstrate that the flow problem of fluids controlled by Navier-Stokes equations can be well solved through the Least-squares finite element method.