A Multiple-Invariants Preserving Scheme for Modified Two-Component Euler-Poincaré Equations

Abstract

This paper presents a high-order multiple-invariants preserving numerical scheme for the modified Euler-Poincaré equations with two components. It is shown that the scheme preserves at least three invariants: mass, momentum and energy. In contrast, the previous schemes usually keep only one or two. Meanwhile, the scheme achieves high order accuracy in spatial direction as well as second-order in time, which will be proved rigorously in this paper. The key to the present scheme aims at the construction of a bi-variate function and utilization of a special time discretization. Numerical tests are given to verify the theoretical findings.