Meshless Methods In Computational Fluid Dynamics Applied Research

Meshfree/meshless method is a kind of recently proposed novel numerical tool for solving partial differential equations. This method requires only nodes, and no element connectivity is needed, thus, it totally avoids degradation of accuracy as well as complexity in programming owing to remesh in each step of evolution in the conventional computational methods. So meshfree methods have gained significant attention in the computational mechanics community.The meshfree methods have got the application in the fields of solid mechanics and materials mechanics, but still are less involved in the field of fluid mechanic and numerical heat transfer. In this paper, meshfree method is researched and applied to many fluid dynamics and heat transfer problems. The main contents of this paper are summarized as follows:The paper first presents an overview of meshless methods in computational fluid dynamics. Following systematically introduces knowledge about meshfree techniques, including the approximation of meshless methods, the selection of weight function, the methods of numerical integral and treatments of essential boundary conditions, etc.Transient heat conduction problems are solved by Element Free Galerkin Method combined the θ family of methods and the numerical results show the validity and flexibility of the Element Free Galerkin Method.It is well known that numerical solutions of conventional methods may be corrupted by non-physical oscillations when the non-symmetric convection action dominates the diffusion action in the transport problems. In order to eliminate spurious oscillations, some new stability methods are constructed. As far as steady convection diffusion is concerned, all kinds of meshfree methods such as Meshfree Streamline Upwind Petrov-Galerkin (MFSUPG) Method, Meshfree Galerkin/Least Squares (MFGLS) Method and Meshfree Sub-Grid Scale (MFSGS) Method are constructed;for unsteady convection diffusion problems, besides the above stability methods, Meshfree Least-Squares (MFLS) Method is also considered. The efficiency of these methods used for convection dominated problems are observed by several presented numerical examples, which show that these methods have high accuracy and good stabilization since spurious oscillations can be largely restrained.The application of the meshfree methods are extended to non-Newtonian flow problems, which successfully simulate the heat transfer problem of flowing polymer melts. Temperature profiles are obtained for different tube lengths, comparied with the no viscous dissipation model, which shows that the temperature-dependent viscous dissipation term had significantly impact on the heat transfer, i.e., the temperature difference between the model with temperature-dependent power-law viscous dissipation and the model without viscous dissipation is about 64 °C. Moreover, the limiting temperature profiles of both no viscosity dissipation model and temperature-dependent power-law model are influenced by the wall boundary, but not by the inlet conditions of the molten.