In this talk, we will present the construction and theory of numerical methods for physical problems in general orthogonal curvilinear coordinates and prove that a Poisson-bracket structure can still be obtained after applying the appropriate finite element discretizations. However, the Hamiltonian systems in the new coordinate systems generally cannot be decomposed into subsystems that can be solved exactly, thus in this talk we will propose a semi-implicit numerical method. This method has been applied to solve the problem under strong magnetic fields and its asymptotic stability will be analyzed.