It is shown in the literature that an energy law preserving method will perform better for multiphase problems.
Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models.
We also demonstrate that when applying the energy law preserving method to the model of Cahn Hilliard type, un-physical interfacial oscillations may occur.
We use the idea in [33] to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen Cahn and Cahn Hilliard type, respectively, governing the motion of two-phase incompressible flows.
The partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems.
In this paper, we give several systematic methods for discretizing general multi-symplectic formulations of Hamiltonian PDEs, including a local energy-preserving algorithm, a class of global energy-preserving methods and a local momentum-preserving algorithm.
It is shown that the proposed approach allows us to obtain the energy-preserving methods derived in [12] by Cohen and Hairer (2011) and in [1] by Brugnano et al. (2012) for Poisson systems.
Within this class of methods, two second-order algorithms are designed under the requirement of attaining non-linear unconditional stability: the energy preserving (EP) and energy decaying (ED) methods.
Finally, the core of this work is a novel LES strategy based on split form DG methods that are kinetic energy preserving.
Lately, Furihata and Matsuo have developed the so-called "discrete variational derivative method" that automatically constructs energy preserving or dissipative finite difference schemes.
Thus, it has to seek the balance between target energy preserving and intrusion energy removing.
