Maojun Li

Maojun Li, Liwei Xu, Yongping Cheng

In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudo-conservative system and a set of pseudo-elliptic equations. Since the pseudo-conservative system is no longer hyperbolic and its Riemann problem can only be approximately solved, we consider the utilization of the central discontinuous Galerkin method which possesses an important feature of needlessness of Riemann solvers. Meanwhile, the stationary elliptic part will be solved using the finite element method. Both the well-balanced and the positivity-preserving features which are highly desirable in the simulation of the shallow water wave will be embedded into the proposed numerical scheme. The accuracy and efficiency of the numerical model and method will be illustrated through numerical tests.

Jun She, Haiyun Dong, Maojun Li et al.

In this paper, we present a numerical scheme designed for coupled systems of variable-topography shallow water flow and solute transport. By integrating a variable-density system with an expression for relative density of mixtures, a novel formulation of the coupled system is derived. To ensure the well-balanced property, auxiliary variables are introduced to reformulate the variable-density shallow water equations into a new form, which is then discretized using the discontinuous Galerkin (DG) method with the Lax-Friedrichs (LF) flux as the numerical flux. By selecting appropriate values for the auxiliary variables, we demonstrate that the proposed method accurately preserves steady-state solutions under still water conditions, thereby verifying its well-balanced nature. Furthermore, sufficient conditions for preserving the positivity of both water depth and concentration are proposed and rigorously proven. A positivity-preserving limiter is introduced to enforce these conditions. Finally, a series of numerical examples are conducted to validate the computational accuracy and effectiveness of the proposed method.

Haoran Lin, Wenrui Chen, Xianchi Chen et al.

Dexterous grasp datasets are vital for embodied intelligence, but mostly emphasize grasp stability, ignoring functional grasps needed for tasks like opening bottle caps or holding cup handles. Most rely on bulky, costly, and hard-to-control high-DOF Shadow Hands. Inspired by the human hand's underactuated mechanism, we establish UniFucGrasp, a universal functional grasp annotation strategy and dataset for multiple dexterous hand types. Based on biomimicry, it maps natural human motions to diverse hand structures and uses geometry-based force closure to ensure functional, stable, human-like grasps. This method supports low-cost, efficient collection of diverse, high-quality functional grasps. Finally, we establish the first multi-hand functional grasp dataset and provide a synthesis model to validate its effectiveness. Experiments on the UFG dataset, IsaacSim, and complex robotic tasks show that our method improves functional manipulation accuracy and grasp stability, enables efficient generalization across diverse robotic hands, and overcomes annotation cost and generalization challenges in dexterous grasping. The project page is at https://haochen611.github.io/UFG.