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In this paper, the quantum hydrodynamic equations (Quantum Hydrodynamic System) format Quasineutral asymptotic limit, the following equations in this model there is an important physical quantity: Debye length (the Debye length), which is a measure of a unit length of a charge imbalance, Our concern is when the Debye length tends to zero situation. Currently there are many systems on the numeric format of this literature, but more or less inadequate. When we use the display format, the time-step size and asked space step must be small enough to ensure a stable form, so that will be a very large amount of computation. Typically, there are two implicit method: direct implicit scheme and implicit method of moments, these two methods, there are many literature, as in [9]. However, in some areas when using these methods still require a small time step, therefore, to overcome the small time-step method is extremely necessary. In this paper we will present \Furthermore, even if this format is implicit, but it is the explicit computation format is the same, not a large amount of computation. Next, we introduce the framework of this article. This paper is divided into three chapters, the first chapter is an introduction to introduce relevant background as well as to consider the issue of the physical and mathematical significance. In the second chapter, describes the quantum fluid power systems Debye length zero asymptotically equivalent form model and the derivation of the Poisson equation, and finally get the Poisson equation equivalent form which, ▽ 2 : for the two order derivative tensor product. Then we discuss the equation of time and space discretization, which proposed asymptotic form, q is the momentum ρu Because this format involves a three time level value, we must use the classical format for the first and second iteration . And classical format, the asymptotic form with three differences, first of all, equation (0.6) is an elliptic problem, assuming the first layer of n time all values ??are known, the use of (0.6) formula can calculate n 1 layer Φ n 1 , then equation (0.5) computing a second equation q n 1 , and finally with a first a formula calculating time layer n 1 ρ values. Additionally, this format when dealing with electric source term is not fully implicit, but in (0.5) with the right type of semi-implicit term ρ n ▽ Φ n 1 to approximate ρ ▽ Φ. If fully implicit form ρ n 1 ▽ Φ n 1 , then, in the calculation of q n 1 requires n 1 time layer density value, which is a bad trend. In fact, the fully implicit format is unnecessary (see ref. [2]). Finally, it should be noted that the relaxation term is composed of two layers, the average time to the approximation. And it is worth mentioning that the asymptotic form of classical format has the same amount of computation. In the third chapter, we give the asymptotic form and classical format and gives examples illustrate contrast, typical examples of which steady-state solution of the perturbed situation. Known W 0 = (ρ 0 = 1, q 0 = 1, Φ 0 = 0), area (0,1), the Euler system is periodic boundary conditions to Dirichlet boundary condition Poisson equation, assuming disturbance W 0 satisfies the following condition where, δ = 10 -2 is the perturbation amplitude, we selected the parameters are as follows: γ = 5/3, ε = 0.01, and λ = 0.01, ie ω = 10 3 . For small time steps, we will see the asymptotic form of classical format with the same result. When △ t ≥ ω -1 , the classical explicit scheme is unstable, and the asymptotic form is stable. The following is a comparison chart.
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