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
The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical symmetry properties of the numerical schemes are discusse...The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical symmetry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian(ALE)method. Numerical results are presented to compare three discrete configurations, i.e.,the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometrical source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.展开更多
Solidifi cation shrinkage has been recognized as an important factor for macrosegregation formation. An arbitrary Lagrangian–Eulerian(ALE) model is constructed to predict the macrosegregation caused by thermal–solut...Solidifi cation shrinkage has been recognized as an important factor for macrosegregation formation. An arbitrary Lagrangian–Eulerian(ALE) model is constructed to predict the macrosegregation caused by thermal–solutal convection and solidi-fi cation shrinkage. A novel mesh update algorithm is developed to account for the domain change induced by solidifi cation shrinkage. The velocity–pressure coupling between the non-homogenous mass conservation equation and momentum equation is addressed by a modifi ed pressure correction method. The governing equations are solved by the streamline-upwind/Petrov–Galerkin-stabilized fi nite element algorithm. The application of the model to the Pb-19.2 wt%Sn alloy solidifi cation problem is considered. The inverse segregation is successfully predicted, and reasonable agreement with the literature results is obtained. Thus, the ALE model is established to be a highly effective tool for predicting the macrosegregation caused by solidifi cation shrinkage and thermal–solutal convection. Finally, the effect of solidifi cation shrinkage is analyzed. The results demonstrate that solidifi cation shrinkage delays the advance of the solidifi cation front and intensifi es the segregation.展开更多
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Project supported by the National Natural Science Foundation of China(Nos.11471048 and U1630249)the Foundation of Chinese Academy of Engineering Physics(No.2014A0202010)the Foundation of Laboratory of Computational Physics(No.9140C690202140C69293)
文摘The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical symmetry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian(ALE)method. Numerical results are presented to compare three discrete configurations, i.e.,the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometrical source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.
基金supported by the National Natural Science Foundation of China-Liaoning Joint Fund (U1508215)
文摘Solidifi cation shrinkage has been recognized as an important factor for macrosegregation formation. An arbitrary Lagrangian–Eulerian(ALE) model is constructed to predict the macrosegregation caused by thermal–solutal convection and solidi-fi cation shrinkage. A novel mesh update algorithm is developed to account for the domain change induced by solidifi cation shrinkage. The velocity–pressure coupling between the non-homogenous mass conservation equation and momentum equation is addressed by a modifi ed pressure correction method. The governing equations are solved by the streamline-upwind/Petrov–Galerkin-stabilized fi nite element algorithm. The application of the model to the Pb-19.2 wt%Sn alloy solidifi cation problem is considered. The inverse segregation is successfully predicted, and reasonable agreement with the literature results is obtained. Thus, the ALE model is established to be a highly effective tool for predicting the macrosegregation caused by solidifi cation shrinkage and thermal–solutal convection. Finally, the effect of solidifi cation shrinkage is analyzed. The results demonstrate that solidifi cation shrinkage delays the advance of the solidifi cation front and intensifi es the segregation.
