On the design of non-singular, energy-momentum consistent integrators for nonlinear dynamics using energy splitting and perturbation techniques

Liu，Ju1,2

2023-08-15

10.1016/j.jcp.2023.112177

Journal of Computational Physics   影响因子和分区

0021-9991

1090-2716

This work proposes a suite of numerical techniques to facilitate the design of structure-preserving integrators for nonlinear dynamics, with particular emphasis on many-body dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt a difference quotient formula in their algorithmic force definitions, which suffers from numerical instability as the denominator gets close to zero. There is a need to develop structure-preserving integrators without invoking the quotient formula. In this work, the potential energy of a Hamiltonian system is split into two parts, and specially developed quadrature rules are applied separately to them. The resulting integrators can be regarded as classical ones perturbed with first- or second-order terms, and the energy split guarantees the dissipative nature in the numerical residual. In the meantime, the conservation of invariants is respected in the design. A complete analysis of the proposed integrators is given, with representative numerical examples provided to demonstrate their performance. They can be used either independently as energy-decaying and momentum-conserving schemes for nonlinear problems or as an alternate option with a conserving integrator, such as the LaBudde-Greenspan integrator, when the numerical instability in the difference quotient is detected.

Energy-momentum scheme Many-body dynamics Nonlinear dynamics Quadrature Time integration

SCI ; EI

英语

第一 ; 通讯

National Natural Science Foundation of China[12172160];Southern University of Science and Technology[Y01326127];

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:001000126500001

ACADEMIC PRESS INC ELSEVIER SCIENCE

20231814047289

Design ; Hamiltonians ; Momentum ; Numerical methods ; Potential energy

Mathematics:921 ; Numerical Methods:921.6 ; Mechanics:931.1

PHYSICS

2-s2.0-85154566974

Scopus

1.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
2.Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China

Liu，Ju. On the design of non-singular, energy-momentum consistent integrators for nonlinear dynamics using energy splitting and perturbation techniques[J]. Journal of Computational Physics,2023,487.

Liu，Ju.(2023).On the design of non-singular, energy-momentum consistent integrators for nonlinear dynamics using energy splitting and perturbation techniques.Journal of Computational Physics,487.

Liu，Ju."On the design of non-singular, energy-momentum consistent integrators for nonlinear dynamics using energy splitting and perturbation techniques".Journal of Computational Physics 487(2023).