A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspire...A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspired by the dual-support,a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed.Conventionally,the SPH formulation employs either the influence domain or the support domain.The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH formulation when variable smoothing lengths are used.The DS-SPH formulation can be implemented into conventional SPH codes with minimal changes and also without compromising the computational efficiency.A number of numerical examples involving weakly compressible.fluid are presented to demonstrate the capability of the method.展开更多
In this paper,we present a dual-horizon nonlocal diffusion model,in which the influence area at each point consists of a standard sphere horizon and an irregular dual horizon and its geometry is determined by the dist...In this paper,we present a dual-horizon nonlocal diffusion model,in which the influence area at each point consists of a standard sphere horizon and an irregular dual horizon and its geometry is determined by the distribution of the varying horizon parameter.We prove the mass conservation and maximum principle of the proposed nonlocal model,and establish its well-posedness and convergence to the classical diffusion model.Noticing that the dual horizon-related term in fact vanishes in the corresponding variational formof themodel,we then propose a finite element discretization for its numerical solution,which avoids the difficulty of accurate calculations of integrals on irregular intersection regions between the mesh elements and the dual horizons.Various numerical experiments in two and three dimensions are also performed to illustrate the usage of the variable horizon and demonstrate the effectiveness of the numerical scheme.展开更多
基金The authors acknowledge the supports from the ERC-CoG(Computational Modeling and Design of Lithium-ion Batteries(COMBAT)),RISE-BESTOFRAC and National Science Foundation of China(51474157).
文摘A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspired by the dual-support,a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed.Conventionally,the SPH formulation employs either the influence domain or the support domain.The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH formulation when variable smoothing lengths are used.The DS-SPH formulation can be implemented into conventional SPH codes with minimal changes and also without compromising the computational efficiency.A number of numerical examples involving weakly compressible.fluid are presented to demonstrate the capability of the method.
基金supported by the National Natural Science Foundation of China(Grants 11801533,11871454)Fundamental Research Funds for the Central Universities(Grant 202042008)Natural Science Foundation of Shandong Province(Grant ZR2019ba031).
文摘In this paper,we present a dual-horizon nonlocal diffusion model,in which the influence area at each point consists of a standard sphere horizon and an irregular dual horizon and its geometry is determined by the distribution of the varying horizon parameter.We prove the mass conservation and maximum principle of the proposed nonlocal model,and establish its well-posedness and convergence to the classical diffusion model.Noticing that the dual horizon-related term in fact vanishes in the corresponding variational formof themodel,we then propose a finite element discretization for its numerical solution,which avoids the difficulty of accurate calculations of integrals on irregular intersection regions between the mesh elements and the dual horizons.Various numerical experiments in two and three dimensions are also performed to illustrate the usage of the variable horizon and demonstrate the effectiveness of the numerical scheme.
