A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapp...A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.展开更多
We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity mod...We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann solvers.The scheme preserves constant states for any mesh motion and we also study its positivity preservation property.Local grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large cells.Second,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.展开更多
In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing ac...In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solutions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.展开更多
Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in o...Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.展开更多
In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving meshes.Based on the L^(2) conservation law of KdV equations,we...In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving meshes.Based on the L^(2) conservation law of KdV equations,we adopt the conservative and dissipative numerical fuxes for the nonlinear convection and linear dispersive terms,respectively.Thus,one conservative and three dissipative ALE-DG schemes are proposed for the equations.The invariant preserving property for the conservative scheme and the corresponding dissipative properties for the other three dissipative schemes are all presented and proved in this paper.In addition,the L^(2)-norm error estimates are also proved for two schemes,whose numerical fuxes for the linear dispersive term are both dissipative type.More precisely,when choosing the approximation space with the piecewise kth degree polynomials,the error estimate provides the kth order of convergence rate in L^(2)-norm for the scheme with the conservative numerical fuxes applied for the nonlinear convection term.Furthermore,the(k+1∕2)th order of accuracy can be proved for the ALE-DG scheme with dissipative numerical fuxes applied for the convection term.Moreover,a Hamiltonian conservative ALE-DG scheme is also presented based on the conservation of the Hamiltonian for KdV equations.Numerical examples are shown to demonstrate the accuracy and capability of the moving mesh ALE-DG methods and compare with stationary DG methods.展开更多
An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuou...An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.展开更多
An effective computational method is developed for dynamic analysis offluid-structure interaction problems involving large-amplitude sloshing of the fluid andlarge-displacement motion of the structure. The structure i...An effective computational method is developed for dynamic analysis offluid-structure interaction problems involving large-amplitude sloshing of the fluid andlarge-displacement motion of the structure. The structure is modeled as a rigid container supportedby a system consisting of springs and dashpots. The motion of the fluid is decomposed into twoparts: the large-displacement motion with the container and the large-amplitude sloshing relative tothe container. The former is conveniently dealt with by defining a container-fixed noninertiallocal frame, while the latter is easily handled by adopting an ALE kinematical description. Thisleads to an easy and accurate treatment of both the fluid-structure interface and the fluid freesurface without producing excessive distortion of the computational mesh. The coupling between thefluid and the structure is accomplished through the coupling matrices that can be easilyestablished. Two numerical examples, including a TLD-structure system and a simplified liquid-loadedvehicle system, are presented to demonstrate the effectiveness and reliability of the proposedmethod. The present work can also be applied to simulate fluid-structure problems incorporatingmultibody systems and several fluid domains.展开更多
An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal p...An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal positions and slopes of eight nodes, two material coordinates in the axial direction are used as the generalized coordinates. As a consequence, the nodes in the ALE-ANCF are not associated with any specific material points and the axial length of the solid element can be varied over time. These two material coordinates give rise to a variable mass matrix and an additional inertial force vector. Computationally efficient formulae of the additional inertial forces and elastic forces, as well as their Jacobians, are also derived. The dynamic equation of a flexible multibody system (FMBS) with variable-length bodies is presented. The maximum and minimum lengths of the boundary elements of an FMBS have to be appropriately defined to ensure accuracy and non-singularity when solving the dynamic equation. Three numerical examples of static and dynamic problems are given to validate the variable-length solid elements of ALE-ANCF and show their capability.展开更多
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as th...A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.展开更多
基金Project supported by the China Postdoctoral Science Foundation(No.2017M610823)
文摘A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.
文摘We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann solvers.The scheme preserves constant states for any mesh motion and we also study its positivity preservation property.Local grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large cells.Second,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.
基金the fellowship of China Postdoctoral Science Foundation,no:2020TQ0030.Y.Xu:Research supported by National Numerical Windtunnel Project NNW2019ZT4-B08+1 种基金Science Challenge Project TZZT2019-A2.3NSFC Grants 11722112,12071455.X.Li:Research supported by NSFC Grant 11801062.
文摘In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solutions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.
基金the support received from the Laoshan Laboratory(No.LSKJ202202000)the National Natural Science Foundation of China(Grant Nos.12032002,U22A20256,and 12302253)the Natural Science Foundation of Beijing(No.L212023)for partially funding this work.
文摘Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.
基金This work was supported by the National Numerical Windtunnel Project NNW2019ZT4-B08Science Challenge Project TZZT2019-A2.3the National Natural Science Foundation of China Grant no.11871449.
文摘In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving meshes.Based on the L^(2) conservation law of KdV equations,we adopt the conservative and dissipative numerical fuxes for the nonlinear convection and linear dispersive terms,respectively.Thus,one conservative and three dissipative ALE-DG schemes are proposed for the equations.The invariant preserving property for the conservative scheme and the corresponding dissipative properties for the other three dissipative schemes are all presented and proved in this paper.In addition,the L^(2)-norm error estimates are also proved for two schemes,whose numerical fuxes for the linear dispersive term are both dissipative type.More precisely,when choosing the approximation space with the piecewise kth degree polynomials,the error estimate provides the kth order of convergence rate in L^(2)-norm for the scheme with the conservative numerical fuxes applied for the nonlinear convection term.Furthermore,the(k+1∕2)th order of accuracy can be proved for the ALE-DG scheme with dissipative numerical fuxes applied for the convection term.Moreover,a Hamiltonian conservative ALE-DG scheme is also presented based on the conservation of the Hamiltonian for KdV equations.Numerical examples are shown to demonstrate the accuracy and capability of the moving mesh ALE-DG methods and compare with stationary DG methods.
基金supported in part by a“Computational R&D in Support of Stockpile Stewardship”Grant from Lawrence Livermore National Laboratorythe National Science Foundation Grants DMS-1619892+2 种基金the Air Force Office of Scientifc Research,USAF,under Grant/contract number FA9955012-0358the Army Research Office under Grant/contract number W911NF-15-1-0517the Spanish MCINN under Project PGC2018-097565-B-I00
文摘An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.
基金This project is supported by National 863 Hi-Tech Project Foundation (No. 2002AA411030).
文摘An effective computational method is developed for dynamic analysis offluid-structure interaction problems involving large-amplitude sloshing of the fluid andlarge-displacement motion of the structure. The structure is modeled as a rigid container supportedby a system consisting of springs and dashpots. The motion of the fluid is decomposed into twoparts: the large-displacement motion with the container and the large-amplitude sloshing relative tothe container. The former is conveniently dealt with by defining a container-fixed noninertiallocal frame, while the latter is easily handled by adopting an ALE kinematical description. Thisleads to an easy and accurate treatment of both the fluid-structure interface and the fluid freesurface without producing excessive distortion of the computational mesh. The coupling between thefluid and the structure is accomplished through the coupling matrices that can be easilyestablished. Two numerical examples, including a TLD-structure system and a simplified liquid-loadedvehicle system, are presented to demonstrate the effectiveness and reliability of the proposedmethod. The present work can also be applied to simulate fluid-structure problems incorporatingmultibody systems and several fluid domains.
基金the National Natural Science Foundation of China (Grants 11521062, 11722216)the 111 China Project (Grant B16003)+1 种基金Postgraduate Research and Practice Innovation Program of Jiangsu Province (Grant KYCX17_0226)China Scholarship Council.
文摘An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal positions and slopes of eight nodes, two material coordinates in the axial direction are used as the generalized coordinates. As a consequence, the nodes in the ALE-ANCF are not associated with any specific material points and the axial length of the solid element can be varied over time. These two material coordinates give rise to a variable mass matrix and an additional inertial force vector. Computationally efficient formulae of the additional inertial forces and elastic forces, as well as their Jacobians, are also derived. The dynamic equation of a flexible multibody system (FMBS) with variable-length bodies is presented. The maximum and minimum lengths of the boundary elements of an FMBS have to be appropriately defined to ensure accuracy and non-singularity when solving the dynamic equation. Three numerical examples of static and dynamic problems are given to validate the variable-length solid elements of ALE-ANCF and show their capability.
文摘A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
