METHOD FOR ADAPTIVE MESH GENERATION BASED ON GEOMETRICAL FEATURES OF 3D SOLID

In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defmed criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delatmay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.

Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs:Applications to Compressible Euler Equations and Granular Hydrodynamics

We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.

AnAdaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics

This paper extends the adaptive moving mesh method developed by Tang and Tang[36]to two-dimensional(2D)relativistic hydrodynamic(RHD)equations.The algorithm consists of two“independent”parts:the time evolution of the RHD equations and the(static)mesh iteration redistribution.In the first part,the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations.The second part is an iterative procedure.In each iteration,the mesh points are first redistributed,and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way.Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.

An Adaptive Moving Mesh Method for the Five-Equation Model

The five-equation model of multi-component flows has been attracting much attention among researchers during the past twenty years for its potential in the study of the multi-component flows.In this paper,we employ a second order finite volume method with minmod limiter in spatial discretization,which preserves local extrema of certain physical quantities and is thus capable of simulating challenging test problems without introducing non-physical oscillations.Moreover,to improve the numerical resolution of the solutions,the adaptive moving mesh strategy proposed in[Huazhong Tang,Tao Tang,Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws,SINUM,41:487-515,2003]is applied.Furthermore,the proposed method can be proved to be capable of preserving the velocity and pressure when they are initially constant,which is essential in material interface capturing.Finally,several classical numerical examples demonstrate the effectiveness and robustness of the proposed method.

Remapping-Free Adaptive GRP Method for Multi-Fluid Flows I:One Dimensional Euler Equations

In this paper,a remapping-free adaptive GRP method for one dimensional(1-D)compressible flows is developed.Based on the framework of finite volume method,the 1-D Euler equations are discretized on moving volumes and the resulting numerical fluxes are computed directly by the GRP method.Thus the remapping process in the earlier adaptive GRP algorithm[17,18]is omitted.By adopting a flexible moving mesh strategy,this method could be applied for multi-fluid problems.The interface of two fluids will be kept at the node of computational grids and the GRP solver is extended at the material interfaces of multi-fluid flows accordingly.Some typical numerical tests show competitive performances of the new method,especially for contact discontinuities of one fluid cases and the material interface tracking of multi-fluid cases.

Lattice Boltzmann method for simulating particle-fluid interactions

The lattice Boltzmann method （LBM） has gained increasing popularity in the last two decades as an alternative numerical approach for solving fluid flow problems. One of the most active research areas in the LBM is its application in particle-fluid systems, where the advantage of the LBM in efficiency and parallel scalability has made it superior to many other direct numerical simulation （DNS） techniques. This article intends to provide a brief review of the application of the LBM in particle-fluid systems. The numerical techniques in the LBM pertaining to simulations of particles are discussed, with emphasis on the advanced treatment for boundary conditions on the particle-fluid interface. Other numerical issues, such as the effect of the internal fluid, are also briefly described. Additionally, recent efforts in using the LBM to obtain closures for particle-fluid drag force are also reviewed.

Numerical study on the morphology of a liquid-liquid pintle injector element primary breakup spray

Primary breakup in a liquid-liquid pintle injector element at different radial jet velocities is investigated to elucidate the impingement morphology,the formation of primary breakup spray half cone angle,the pressure distribution,the liquid diameter distribution,and the liquid velocity distribution.With a sufficient mesh resolution,the liquid morphology can be captured in a physically sound way.A mushroom tip is triggered by a larger radial jet velocity and breakup happens at the tip edge first.Different kinds of ligament breakup patterns due to aerodynamic force and surface tension are captured on the axial sheet.A high pressure core is spotted at the impinging point region.A larger radial jet velocity can feed more disturbances into the impinging point and the axial sheet,generate stronger vortices to promote the breakup process at a longer distance,and form a larger spray half cone angle.Because of the re-collision phenomenon the axial sheet diameter does not decrease monotonically.The inner rim on the axial sheet shows a larger diameter magnitude and a lower velocity magnitude due to surface tension.This paper is expected to provide a reference for the optimum design of a liquid-liquid pintle injector.

Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a ＂volume of fluid＂ type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.