Research On 2D Unstructured Mesh Navier-Stokes Equation Solver Based On Feni CS

With the dramatic increase in computing speed and storage capacity of modern computing clusters,virtual integrated modern computational fluid dynamics systems based on numerical pools for analysis,assessment,forecasting,and optimization are being developed for the navigational performance of marine vessels in complex marine environments.Research on these numerical techniques provide the necessary virtual testing environment and computing means.Under complex geometric shapes,unstructured grids could complete pre-processing work quickly and achieve a certain degree of numerical accuracy,which is the mainstream of modern CFD technology development and application.The finite element method has good adaptability on complex boundary conditions and unstructured grids.which is one of the mainstream numerical methods for solving Navier-Stokes equations.The finite element method has important research and application value to solve fluid problems.The paper uses Python language and implement operator splitting schemes based on FEniCS and other scientific computing libraries.It compares the computational accuracy,efficiency,and stability of convection dominance problems with different stabilization schemes.Based on sadjoint theory,a suitable unstructured grid adaptive finite element method is developed,to optimizes the grid that is sensitive to the objective function,to simplify the unstructured grid preprocessing,and to improve the calculation accuracy of the flow-around problem.In paper,a consistent splitting scheme is applied to the adaptive finite element method,which simplifies the error term.Compared with the classical projection method and the incremental pressure correction format,the computational accuracy and efficiency in this new adaptation algorithm are improved.The main content of this paper is as follows: 1.The mathematical and symbol specification of the finite element in the functional space and the weak form derivation of the Navier-Stokes equations are given.Appropriate operator splitting format is used to build the variational form of the pressure field and the velocity field.The appropriate mixing elements are selected for the pressure field-velocity field,and the finite element method is verified in numerical accuracy of cavity flow and flow around cylinder.2.The convection dominance problem in mixed finite elements is discussed,as well as two commonly used stabilization methods to suppress convection dominance,namely the artificial stickiness method and the SUPG method.In the convection equation,the standard Galerkin method and the above stabilization methods are compared and discussed in terms of calculation accuracy and computational efficiency.Finally,the calculation of the above three methods in the flow field in the critical region is discussed.3.Based on the consistent splitting scheme,an unstructured grid adaptive module based on error indicators was developed for the problem of insufficient mesh density at the boundary of the object and applied to the finite element flow field solver.The ratio of grid adaption was discussed.Error analysis of the number of iterations of the adaption and the initial grid density on the flow around the cylinder.The error indicator is constructed according to different goal function.This paper finds that the calculation error of the flow around cylinder/cuboid of different error indicators exists significant differences.Finally,the computational efficiency and calculation accuracy of different splitting schemes in calculations of flow around cuboid are discussed.In this paper,based on the predecessors’ existing work and the difficulties in solving the problem of incompressible Navier-Stokes equations,efficient and stable stabilization method and grid adaption are programmed.Adaptive algorithm can be used to solve the common fluid problems in ships and marine engineering,and help structural design and optimization.