A two-dimensional numerical wave flume based on SA-MPLS method

A spatially adaptive (SA) two-dimensional (2-D) numerical wave flume is presented based on the quadtree mesh system,in which a new multiple particle level set (MPLS) method is proposed to solve the problem of interface tracking,in which common intersection may be traversed by multiple interfaces.By using the adaptive mesh technique and the MPLS method,mesh resolution is updated automatically with time according to flow characteristics in the modeling process with higher resolution around the free surface and the solid boundary and lower resolution in less important area.The model has good performance in saving computer memory and CPU time and is validated by computational examples of small amplitude wave,second-order Stokes wave and cnoidal wave.Computational results also indicate that standing wave and wave overtopping are also reasonably simulated by the model.

An h-adaptive numerical manifold method for solid mechanics problems

The numerical manifold method(NMM) features its dual cover systems, namely the mathematical cover and physical cover,which provide a unified framework for mechanics problems involving continuum and discontinuum deformation. Uniform finite element meshes can be and are usually used to construct the mathematical cover. Though this strategy can handle different kinds of problems in a unified way, it is not economical for cases with steep deformation gradients or singularities. In this paper, using the recovery-based error estimator, an h-adaptive NMM on quadtree meshes is proposed to deal with such cases. The quadtree meshes serve as the mathematical meshes, on which the local refinement is carried out. When the quadtree meshes are refined,the corresponding mathematical cover, physical cover and manifold elements are updated accordingly. To handle the hanging nodes in the quadtree meshes, we resort to mean value coordinates. Comparing to the refinement based on manifold elements,the proposed strategy guarantees consistent structured meshes throughout the adaptive process, thus retaining the unique feature of original NMM. In contrast with polygonal finite element method, an advantage of the proposed method is that the meshes do not need to conform to the crack face and material boundary, which means the adaptive NMM is very suitable for problems with complex geometric boundary. Several representative mechanics problems, including crack problems, are analyzed to investigate the effectiveness of the proposed method. It is demonstrated that the proposed adaptive NMM has higher accuracy and better performance comparing to uniform refinement strategy.