Structure preserving integration of 3D dissipative bi-Hamiltonian/Nambu systems

Abstract

A structure-preserving splitting integrator is developed for 3D dissipative bi-Hamiltonian/Nambu systems. The integrator uses Strang splitting for conservative and dissipative parts. For Nambu systems, the divergence-free, conservative part is integrated using the energy/volume-preserving Kahan's method, and the dissipative part is integrated by the forward and backward Euler methods. For dissipative bi-Hamiltonian systems, the conservative part is integrated with the energy-preserving average vector field (AVF) method. In both cases, the Hamiltonians of the conservative parts are preserved in the Lorenz, Chen, and Rabinovich systems. The periodic and chaotic solutions are computed accurately by the conservative-dissipative Strang splitting approach.