June  2009, 11(4): 855-874. doi: 10.3934/dcdsb.2009.11.855

Lifting in equation-free methods for molecular dynamics simulations of dense fluids

1. 

Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium, Belgium, Belgium, Belgium

2. 

Polymer Research Division, Department of Chemistry, K.U.Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium, Belgium

Received  July 2008 Revised  October 2008 Published  April 2009

Within the context of multiscale computations, equation-free methods have been developed. In this approach, the evolution of a system is simulated on the macroscopic level while only a microscopic model is explicitly available. To this end, a coarse time stepper for the macroscopic variables can be constructed, based on appropriately initialized microscopic simulations. In this paper, we investigate the initialization of the microscopic simulator using the macroscopic variables only (called lifting in the equation-free framework) when the microscopic model is a molecular dynamics (MD) description of a mono-atomic dense fluid. We assume a macroscopic model to exist in terms of the lowest order velocity moments of the particle distribution (density, velocity and temperature). The major difficulty is to design a lifting operator that accurately reconstructs the physically correct state of the fluid (i.e., the higher order moments) at a reasonable computational cost. We construct a lifting operator, as well as a restriction operator for the reverse mapping. For a simple model problem, we perform a systematic numerical study to assess the time scales on which the lifting errors disappear after reinitialization (healing); we also examine the effects on the simulated macroscopic behavior. The results show that, although in some cases accurate initialization of the higher order moments is not crucial, in general a detailed study of the lifting operator is required.
Citation: Yves Frederix, Giovanni Samaey, Christophe Vandekerckhove, Ting Li, Erik Nies, Dirk Roose. Lifting in equation-free methods for molecular dynamics simulations of dense fluids. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 855-874. doi: 10.3934/dcdsb.2009.11.855
[1]

José Luis López. A quantum approach to Keller-Segel dynamics via a dissipative nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020376

[2]

Neng Zhu, Zhengrong Liu, Fang Wang, Kun Zhao. Asymptotic dynamics of a system of conservation laws from chemotaxis. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 813-847. doi: 10.3934/dcds.2020301

[3]

Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020316

[4]

Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020045

[5]

Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020339

[6]

Shao-Xia Qiao, Li-Jun Du. Propagation dynamics of nonlocal dispersal equations with inhomogeneous bistable nonlinearity. Electronic Research Archive, , () : -. doi: 10.3934/era.2020116

[7]

Ebraheem O. Alzahrani, Muhammad Altaf Khan. Androgen driven evolutionary population dynamics in prostate cancer growth. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020426

[8]

Marc Homs-Dones. A generalization of the Babbage functional equation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 899-919. doi: 10.3934/dcds.2020303

[9]

A. M. Elaiw, N. H. AlShamrani, A. Abdel-Aty, H. Dutta. Stability analysis of a general HIV dynamics model with multi-stages of infected cells and two routes of infection. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020441

[10]

Peter Poláčik, Pavol Quittner. Entire and ancient solutions of a supercritical semilinear heat equation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 413-438. doi: 10.3934/dcds.2020136

[11]

Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020345

[12]

Stefano Bianchini, Paolo Bonicatto. Forward untangling and applications to the uniqueness problem for the continuity equation. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020384

[13]

Anh Tuan Duong, Phuong Le, Nhu Thang Nguyen. Symmetry and nonexistence results for a fractional Choquard equation with weights. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 489-505. doi: 10.3934/dcds.2020265

[14]

Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

[15]

Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 1503-1528. doi: 10.3934/era.2020079

[16]

Cheng He, Changzheng Qu. Global weak solutions for the two-component Novikov equation. Electronic Research Archive, 2020, 28 (4) : 1545-1562. doi: 10.3934/era.2020081

[17]

Hirokazu Ninomiya. Entire solutions of the Allen–Cahn–Nagumo equation in a multi-dimensional space. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 395-412. doi: 10.3934/dcds.2020364

[18]

Jiaquan Liu, Xiangqing Liu, Zhi-Qiang Wang. Sign-changing solutions for a parameter-dependent quasilinear equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020454

[19]

Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020448

[20]

Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020432

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (6)

[Back to Top]