Mesh motion strategy is one of the key points in many fluid-structure interaction problems. One popular technique used to solve this problem is known as the spring analogy method. In this paper a new mesh update approach based on the spring analogy method is presented for the effective treatment of mesh moving boundary problems. The proposed mesh update technique is developed to avoid the generation of squashed invalid elements and maintain mesh quality by considering each element shape and grid scale to the definition of the spring stiffness. The method is applied to several 2D and 3D boundary correction problems for fully unstructured meshes and evaluated by a mesh quality indicator. With these applications,it is demonstrated that the present method preserves mesh quality even under large motions of bodies. We highlight the advantages of this method with respect to robustness and mesh quality.
An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and lid- driven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.
Smoothed particle hydrodynamics (SPH) is a useful meshless method.The first and second orders are the most popular derivatives of the field function in the mechanical governing equations.New methods were proposed to improve accuracy of SPH approximation by the lemma proved.The lemma describes the relationship of functions and their SPH approximation.Finally,the error comparison of SPH method with or without our improvement was carried out.
